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On the dynamics and optimal control of a mathematical model of neuroblastoma and its treatment: Insights from a mathematical model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-16 José García Otero, Mariusz Bodzioch, Juan Belmonte-Beitia
Celyvir is an advanced therapy medicine, consisting of mesenchymal stem cells (MSCs) containing the oncolytic virus ICOVIR 5. This paper sets out a dynamic system which attempts to capture the fundamental relationships between cancer, the immune system and adenoviruses. Two forms of treatment were studied: continuous and periodic, the second being closer to the real situation. In the analysis of the
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Pedestrian models with congestion effects Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-15 Pedro Aceves-Sánchez, Rafael Bailo, Pierre Degond, Zoé Mercier
We study the validity of the dissipative Aw–Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behavior. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution
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Macroscopic modeling of social crowds Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-15 Livio Gibelli, Damián A. Knopoff, Jie Liao, Wenbin Yan
Social behavior in crowds, such as herding or increased interpersonal spacing, is driven by the psychological states of pedestrians. Current macroscopic crowd models assume that these are static, limiting the ability of models to capture the complex interplay between evolving psychology and collective crowd dynamics that defines a “social crowd”. This paper introduces a novel approach by explicitly
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Active particle methods towards a mathematics of living systems Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-13 Nicola Bellomo, Franco Brezzi
This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods applied to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, vehicle and crowd vehicle
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Moment methods for kinetic traffic flow and a class of macroscopic traffic models Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-06 Raul Borsche, Axel Klar
Starting from a nonlocal version of a classical kinetic traffic model, we derive a class of second-order macroscopic traffic flow models using appropriate moment closure approaches. Under mild assumptions on the closure, we prove that the resulting macroscopic equations fulfill a set of conditions including hyperbolicity, physically reasonable invariant domains and physically reasonable bounds on the
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Time-discrete momentum consensus-based optimization algorithm and its application to Lyapunov function approximation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-05 Seung-Yeal Ha, Gyuyoung Hwang, Sungyoon Kim
In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci.30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification
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The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-03-05 Helmut Harbrecht, Marc Schmidlin, Christoph Schwab
This paper is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between Banach spaces near branches of isolated solutions that are implicitly defined by a residual equation. Under s-Gevrey assumptions on the residual equation, we establish s-Gevrey bounds on the Fréchet derivatives of the locally
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Kinetic theory of active particles meets auction theory Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-27 Carla Crucianelli, Juan Pablo Pinasco, Nicolas Saintier
In this paper we study Nash equilibria in auctions from the kinetic theory of active particles point of view. We propose a simple learning rule for agents to update their bidding strategies based on their previous successes and failures, in first-price auctions with two bidders. Then, we formally derive the corresponding kinetic equations which describe the evolution over time of the distribution of
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Impact of a unilateral horizontal gene transfer on the evolutionary equilibria of a population Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-24 Alejandro Gárriz, Alexis Léculier, Sepideh Mirrahimi
How does the interplay between selection, mutation and horizontal gene transfer modify the phenotypic distribution of a bacterial or cell population? While horizontal gene transfer, which corresponds to the exchange of genetic material between individuals, has a major role in the adaptation of many organisms, its impact on the phenotypic density of populations is not yet fully understood. We study
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Kinetic compartmental models driven by opinion dynamics: Vaccine hesitancy and social influence Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-21 Andrea Bondesan, Giuseppe Toscani, Mattia Zanella
We propose a kinetic model for understanding the link between opinion formation phenomena and epidemic dynamics. The recent pandemic has brought to light that vaccine hesitancy can present different phases and temporal and spatial variations, presumably due to the different social features of individuals. The emergence of patterns in societal reactions permits to design and predict the trends of a
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Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-21 Weizhu Bao, Ying Ma, Chushan Wang
We establish optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and typical power-type nonlinearity f(ρ)=ρσ, where ρ:=|ψ|2 is the density with ψ the wave function and σ>0 the exponent of the nonlinearity. For the first-order Lie–Trotter time-splitting method, optimal L2-norm error bound is proved for L∞-potential and σ>0, and optimal
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Inf–sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-20 Volker John, Xu Li, Christian Merdon, Hongxing Rui
This paper considers the discretization of the Stokes equations with Scott–Vogelius pairs of finite element spaces on arbitrary shape-regular simplicial grids. A novel way of stabilizing these pairs with respect to the discrete inf–sup condition is proposed and analyzed. The key idea consists in enriching the continuous polynomials of order k of the Scott–Vogelius velocity space with appropriately
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Entropy-based convergence rates of greedy algorithms Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-16 Yuwen Li, Jonathan W. Siegel
We present convergence estimates of two types of greedy algorithms in terms of the entropy numbers of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the entropy numbers of the solution manifold in Banach spaces. This contrasts with the classical analysis based on the Kolmogorov n-widths and enables us to obtain direct
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A particle method for non-local advection–selection–mutation equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-14 Frank Ernesto Alvarez, Jules Guilberteau
The well-posedness of a non-local advection–selection–mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such problem by a regularized sum of weighted Dirac masses whose characteristics solve a suitably defined ODE system. The convergence of the particle method over any finite
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An analysis of nonconforming virtual element methods on polytopal meshes with small faces Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-09 Hyeokjoo Park, Do Y. Kwak
In this paper, we analyze nonconforming virtual element methods on polytopal meshes with small faces for the second-order elliptic problem. We propose new stability forms for 2D and 3D nonconforming virtual element methods. For the 2D case, the stability form is defined by the sum of an inner product of approximate tangential derivatives and a weighed L2-inner product of certain projections on the
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Derivation of effective theories for thin 3D nonlinearly elastic rods with voids Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2024-02-09 Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of Γ-convergence. Hereby, we generalize the results of the purely elastic setting [M. G. Mora and S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by Γ-convergence, Calc. Var. Partial Differential Equations18 (2003) 287–305] to a framework of free discontinuity problems
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Necessary and sufficient criteria for existence, regularity, and asymptotic stability of enhanced pullback attractors with applications to 3D primitive equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-08-02 Renhai Wang, Boling Guo, Daiwen Huang
We introduce several new concepts called enhanced pullback attractors for nonautonomous dynamical systems by improving the compactness and attraction of the usual pullback attractors in strong topology spaces uniformly over some infinite time intervals. Then we establish several necessary and sufficient criteria for the existence, regularity and asymptotic stability of these enhanced pullback attractors
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A IETI-DP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-08-02 Monica Montardini, Giancarlo Sangalli, Rainer Schneckenleitner, Stefan Takacs, Mattia Tani
We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows for the consideration of discretizations that do not match on the interfaces. We solve the resulting linear system using a Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method. We are interested in solving the arising patch-local problems
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Conforming and nonconforming virtual element methods for fourth order nonlocal reaction diffusion equation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-24 Dibyendu Adak, Verónica Anaya, Mostafa Bendahmane, David Mora
In this work, we have designed conforming and nonconforming virtual element methods (VEM) to approximate non-stationary nonlocal biharmonic equation on general shaped domain. By employing Faedo–Galerkin technique, we have proved the existence and uniqueness of the continuous weak formulation. Upon applying Brouwer’s fixed point theorem, the well-posedness of the fully discrete scheme is derived. Further
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Asymptotic behavior of a three-dimensional haptotactic cross-diffusion system modeling oncolytic virotherapy Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-22 Yifu Wang, Chi Xu
This paper deals with an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy ut=Δu−∇⋅(u∇v)+μu(1−u)−uz,vt=−(u+w)v,wt=Δw−∇⋅(w∇v)−w+uz,zt=DzΔz−z−uz+βw, in a smoothly bounded domain Ω⊂ℝ3 with β>0, μ>0 and Dz>0. Based on a self-map argument, it is shown that under the assumption βmax{1,∥u0∥L∞(Ω)}<1+(1+1minx∈Ωu0(x))−1, this problem possesses
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Regular solutions of chemotaxis-consumption systems involving tensor-valued sensitivities and Robin type boundary conditions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-22 Jaewook Ahn, Kyungkeun Kang, Jihoon Lee
This paper deals with a parabolic–elliptic chemotaxis-consumption system with tensor-valued sensitivity S(x,n,c) under no-flux boundary conditions for n and Robin-type boundary conditions for c. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity S. One of the main steps is to show that ∇c(⋅,t) becomes tiny in L2(Br(x)∩Ω)
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Global classical solvability and stabilization in a two-dimensional chemotaxis–fluid system with sub-logarithmic sensitivity Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-20 Ji Liu
In this paper, we consider the following system: nt+u⋅∇n=Δn−∇⋅(nχ(c)∇c),ct+u⋅∇c=Δc−cn,ut+κ(u⋅∇)u=Δu+∇P+n∇Φ, in a smoothly bounded domain Ω⊂ℝ2, with κ∈{0,1} and a given function χ(c)=1c𝜃 with 𝜃∈[0,1). It is proved that if κ=1 then for appropriately small initial data an associated no-flux/no-flux/Dirichlet initial-boundary value problem is globally solvable in the classical sense, and that if κ=0
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Analysis of complex chemotaxis models Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-14 Youshan Tao, Michael Winkler
This preface describes motivational aspects related to a special issue focusing on “analysis of complex chemotaxis models”, and briefly discusses the contributions provided by the six papers contained therein.
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Existence of multi-spikes in the Keller–Segel model with logistic growth Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-14 Fanze Kong, Juncheng Wei, Liangshun Xu
The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multi-spiky solutions to the
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Critical mass for Keller–Segel systems with supercritical nonlinear sensitivity Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-14 Xuan Mao, Yuxiang Li
This paper is concerned with the following radially symmetric Keller–Segel systems with nonlinear sensitivity ut=Δu−∇⋅(u(1+u)α−1∇v) and 0=Δv−⨍Ωudx+u, posed on Ω={x∈ℝn:|x|2n. Here we consider the supercritical case α≥2n and show a critical mass phenomenon. Precisely, we prove that there exists a critical mass mc:=mc(n,R,α) such that (1) for arbitrary nonincreasing nonnegative initial data u0(x)=u0(|x|)
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Compressible Euler–Maxwell limit for global smooth solutions to the Vlasov–Maxwell–Boltzmann system Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-06 Renjun Duan, Dongcheng Yang, Hongjun Yu
Two fundamental models in plasma physics are given by the Vlasov–Maxwell–Boltzmann system and the compressible Euler–Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at the kinetic and fluid levels, respectively. It has remained a long-standing open problem to rigorously justify the hydrodynamic limit from the former to the latter
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Global boundedness in a 2D chemotaxis-Navier–Stokes system with flux limitation and nonlinear production Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-07-06 Wei Wang
We consider the chemotaxis-Navier–Stokes system with gradient-dependent flux limitation and nonlinear production: nt+u⋅∇n=Δn−∇⋅(nf(|∇c|2)∇c), ct+u⋅∇c=Δc−c+g(n), ut+(u⋅∇)u+∇P=Δu+n∇ϕ and ∇⋅u=0 in a bounded domain Ω⊂ℝ2, where the flux limitation function f∈C2([0,∞]) and the signal production function g∈C1([0,∞]) generalize the prototypes f(s)=Kf(1+s)−α2 and g(s)=Kgs(1+s)β−1 with Kf,Kg>0, α∈ℝ and β>0.
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Three-species drift-diffusion models for memristors Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-06-29 Clément Jourdana, Ansgar Jüngel, Nicola Zamponi
A system of drift-diffusion equations for the electron, hole, and oxygen vacancy densities in a semiconductor, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet–Neumann boundary conditions. This system describes the dynamics of charge carriers in a memristor device. Memristors can be seen as nonlinear resistors with memory, mimicking the
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An effective model for boundary vortices in thin-film micromagnetics Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-06-21 Radu Ignat, Matthias Kurzke
Ferromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unit-length three-dimensional vector field, the magnetization, that corresponds to the stable states of the micromagnetic energy. Our aim is to analyze a thin film regime that captures the asymptotic behavior of boundary vortices generated by the magnetization and
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Human behavioral crowds review, critical analysis and research perspectives Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-06-06 Nicola Bellomo, Jie Liao, Annalisa Quaini, Lucia Russo, Constantinos Siettos
This paper presents a survey and critical analysis of the mathematical literature on modeling and simulation of human crowds taking into account behavioral dynamics. The main focus is on research papers published after the review [N. Bellomo and C. Dogbè, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409–463], thus providing important
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Cross-diffusion models in complex frameworks from microscopic to macroscopic Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-06-06 D. Burini, N. Chouhad
This paper deals with the micro–macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in [ N. Bellomo, N. Outada, J. Soler, Y. Tao and M. Winkler, Chemotaxis and cross diffusion models in complex environments: Modeling towards a multiscale vision, Math. Models
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Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-31 Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vázquez
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multi-patch geometries
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Singular patterns in Keller–Segel-type models Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-29 Juan Campos, Carlos Pulido, Juan Soler, Mario Veruete
The aim of this paper is to elucidate the existence of patterns for Keller–Segel-type models that are solutions of the traveling pulse form. The idea is to search for transport mechanisms that describe this type of waves with compact support, which we find in the so-called nonlinear diffusion through saturated flux mechanisms for the movement cell. At the same time, we analyze various transport operators
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Multigrid solvers for isogeometric discretizations of the second biharmonic problem Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-29 Jarle Sogn, Stefan Takacs
We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the authors have developed an analysis for the first biharmonic problem based on Hackbusch’s framework. This analysis can only be extended to the second biharmonic problem if one assumes uniform grids. In this paper, we prove a multigrid
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Non-isothermal non-Newtonian fluids: The stationary case Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-25 Maurizio Grasselli, Nicola Parolini, Andrea Poiatti, Marco Verani
The stationary Navier–Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet-type boundary conditions. The viscosity is supposed to depend on the temperature and the stress depends on the strain through a suitable power law depending on p∈(1,2) (shear thinning case). For this problem we establish the existence of a weak solution
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Numerical modeling of the brain poromechanics by high-order discontinuous Galerkin methods Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-20 Mattia Corti, Paola F. Antonietti, Luca Dede’, Alfio M. Quarteroni
We introduce and analyze a discontinuous Galerkin method for the numerical modeling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral
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Boundedness and large time behavior of solutions of a higher-dimensional haptotactic system modeling oncolytic virotherapy Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-20 Jiashan Zheng, Yuanyuan Ke
This paper is concerned with the higher-dimensional haptotactic system modeling oncolytic virotherapy, which was initially proposed by Alzahrani–Eftimie–Trucu [Multiscale modelling of cancer response to oncolytic viral therapy, Math. Biosci. 310 (2019) 76–95] (see also the survey Bellomo–Outada et al. [Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward
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Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-17 A. Kaltenbach, M. Růžička
In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe–Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Therefore, the result can be interpreted either as a justification of the numerical method or as
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Lack of robustness and accuracy of many numerical schemes for phase-field simulations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-16 Jinchao Xu, Xiaofeng Xu
In this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phase-field modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the first-order fully implicit scheme is the
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Variational multiscale method stabilization parameter calculated from the strain-rate tensor Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-15 Kenji Takizawa, Yuto Otoguro, Tayfun E. Tezduyar
The stabilization parameters of the methods like the Streamline-Upwind/Petrov–Galerkin, Pressure-Stabilizing/Petrov–Galerkin, and the Variational Multiscale method typically involve two local length scales. They are the advection and diffusion length scales, appearing in the expressions for the advective and diffusive limits of the stabilization parameter. The advection length scale has always been
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L1-Theory for Hele-Shaw flow with linear drift Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-11 Noureddine Igbida
The main goal of this paper is to prove L1-comparison and contraction principles for weak solutions of PDE system corresponding to a phase transition diffusion model of Hele-Shaw type with addition of a linear drift. The flow is considered with a source term and subject to mixed homogeneous boundary conditions: Dirichlet and Neumann. The PDE can be focused to model for instance biological applications
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The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-10 Patrick Henning
In this paper, we consider the generalized inverse iteration for computing ground states of the Gross–Pitaevskii eigenvector (GPE) problem. For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross–Pitaevskii operator
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A nonlinear bending theory for nematic LCE plates Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-05-04 Sören Bartels, Max Griehl, Stefan Neukamm, David Padilla-Garza, Christian Palus
In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat reference configuration, the top layer features an eigenstrain that depends on the local liquid crystal orientation. As a consequence, the plate shows non-flat deformations
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Collective behaviors of stochastic agent-based models and applications to finance and optimization Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-04-26 Dongnam Ko, Seung-Yeal Ha, Euntaek Lee, Woojoo Shim
In this paper, we present a survey of recent progress on the emergent behaviors of stochastic particle models which arise from the modeling of collective dynamics. Collective dynamics of interacting autonomous agents is ubiquitous in nature, and it can be understood as a formation of concentration in a state space. The jargons such as aggregation, herding, flocking and synchronization describe such
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Generalized solution and eventual smoothness in a logarithmic Keller–Segel system for criminal activities Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-04-08 Bin Li, Li Xie
This paper focuses on a simplified variant of the Short et al. model, which is originally introduced by Rodríguez, and consists of a system of two coupled reaction–diffusion-like equations — one of which models the spatio-temporal evolution of the density of criminals and the other of which describes the dynamics of the attractiveness field. Such model is apparently comparable to the logarithmic Keller–Segel
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Analysis of divergence free conforming virtual elements for the Brinkman problem Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-04-07 Xuehai Huang, Feng Wang
In this paper, we develop stability analysis, including inverse inequality, L2 norm equivalence and interpolation error estimates, for divergence free conforming virtual elements in arbitrary dimension. A local energy projector based on the local Stokes problem is suggested, which commutes with the divergence operator. After defining a discrete bilinear form and a stabilization involving only the boundary
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Traveling waves for a Fisher-type reaction–diffusion equation with a flux in divergence form Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-04-07 Margarita Arias, Juan Campos
Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves (TWs) move. This value depends on the solution concept being considered. We analyze an extensive class of Fisher-type reaction–diffusion equations with flows in divergence form. We work with regular flows, which may not meet the standard elliptical conditions
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Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-31 Martina Conte, Yvonne Dzierma, Sven Knobe, Christina Surulescu
A multiscale model for glioma spread in brain tissue under the influence of vascularization and vascular endothelial growth factors is proposed. It accounts for the interplay between the different components of the neoplasm and the healthy tissue and it investigates and compares various therapy approaches. Precisely, these involve radiotherapy and chemotherapy in a concurrent or adjuvant manner together
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Multilevel domain uncertainty quantification in computational electromagnetics Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-30 Rubén Aylwin, Carlos Jerez-Hanckes, Christoph Schwab 2 , ‡, Jakob Zech
We continue our study [R. Aylwin, C. Jerez-Hanckes, C. Schwab and J. Zech, Domain uncertainty quantification in computational electromagnetics, SIAM/ASA J. Uncertain. Quant.8 (2020) 301–341] of the numerical approximation of time-harmonic electromagnetic fields for the Maxwell lossy cavity problem for uncertain geometries. We adopt the same affine-parametric shape parametrization framework, mapping
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A mean field game model of firm-level innovation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-29 Matt Barker, Pierre Degond, Ralf Martin, Mirabelle Muûls
Knowledge spillovers occur when a firm researches a new technology and that technology is adapted or adopted by another firm, resulting in a social value of the technology that is larger than the initially predicted private value. As a result, firms systematically under-invest in research compared with the socially optimal investment strategy. Understanding the level of under-investment, as well as
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Convergence of a particle method for a regularized spatially homogeneous Landau equation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-28 José A. Carrillo, Matias G. Delgadino, Jeremy S. H. Wu
We study a regularized version of the Landau equation, which was recently introduced in [J. A. Carrillo, J. Hu, L. Wang and J. Wu, A particle method for the homogeneous Landau equation, J. Comput. Phys. X7 (2020) 100066, 24] to numerically approximate the Landau equation with good accuracy at reasonable computational cost. We develop the existence and uniqueness theory for weak solutions, and we reinforce
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Dual natural-norm a posteriori error estimators for reduced basis approximations to parametrized linear equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-28 P. Edel, Y. Maday
In this work, the concept of dual natural-norm for parametrized linear equations is used to derive residual-based a posteriori error bounds characterized by a 𝒪(1) stability constant. We translate these error bounds into very effective practical a posteriori error estimators for reduced basis approximations and show how they can be efficiently computed following an offline/ online strategy. We prove
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Taylor–Couette flow with temperature fluctuations: Time periodic solutions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-25 Eduard Feireisl, Young-Sam Kwon
We consider the motion of a viscous compressible and heat conducting fluid confined in the gap between two rotating cylinders (Taylor–Couette flow). The temperature of the cylinders is fixed but not necessarily constant. We show that the problem admits a time-periodic solution as soon as the ratio of the angular velocities of the two cylinders is a rational number.
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Fast and slow clustering dynamics of Cucker–Smale ensemble with internal oscillatory phases Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-21 Seung-Yeal Ha, Jeongho Kim, Jinyeong Park
We study fast and slow clustering dynamics of Cucker–Smale ensemble with internal phase dynamics via the Cucker–Smale–Kuramoto (in short, CSK) model. The CSK model describes the emergent dynamics of flocking particles with phase dynamics. It consists of the Cucker–Smale flocking model and the Kuramoto model, and their interplay is registered in the communication weight function between particles. We
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The virtual element method for the 3D resistive magnetohydrodynamic model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-16 Lourenço Beirão da Veiga, Franco Dassi, Gianmarci Manzini, Lorenzo Mascotto
We present a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity
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Elastic stabilization of an intrinsically unstable hyperbolic flow–structure interaction on the 3D half-space Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-13 Abhishek Balakrishna, Irena Lasiecka, Justin T. Webster
The strong asymptotic stabilization of 3D hyperbolic dynamics is achieved by a damped 2D elastic structure. The model is a Neumann wave-type equation with low regularity coupling conditions given in terms of a nonlinear von Karman plate. This problem is motivated by the elimination of aeroelastic instability (sustained oscillations of bridges, airfoils, etc.) in engineering applications. Empirical
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Bound-preserving finite element approximations of the Keller–Segel equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-13 Santiago Badia, Jesús Bonilla, Juan Vicente Gutiérrez-Santacreu
This paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized
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Pressure-relaxation limit for a one-velocity Baer–Nunziato model to a Kapila model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-13 Cosmin Burtea, Timothée Crin-Barat, Jin Tan
In this paper, we study a singular limit problem for a compressible one-velocity bifluid system. More precisely, we show that solutions of the Kapila system generated by initial data close to equilibrium are obtained in the pressure-relaxation limit from solutions of the Baer–Nunziato (BN) system. The convergence rate of this process is a consequence of our stability result. Besides the fact that the
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Well-posedness of a Navier–Stokes–Cahn–Hilliard system for incompressible two-phase flows with surfactant Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-13 Andrea Di Primio, Maurizio Grasselli, Hao Wu
We investigate a diffuse-interface model that describes the dynamics of viscous incompressible two-phase flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn–Hilliard equation for the difference of local concentrations of the binary fluid mixture coupled with a fourth-order Cahn–Hilliard equation for the local concentration of the surfactant.
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Entropy dissipation and propagation of chaos for the uniform reshuffling model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 2023-03-13 Fei Cao, Pierre-Emmanuel Jabin, Sebastien Motsch 3 , *
We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of mean-field type and eventually leads to a exponential distribution of wealth. To better understand this dynamics, we investigate its limit as the number of agents goes to infinity. We prove rigorously the so-called propagation