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On the continuum limit of epidemiological models on graphs: Convergence and approximation results Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240430
Blanca Ayuso de Dios, Simone Dovetta, Laura V. SpinoloWe focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of graphons we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations.

A nodally boundpreserving finite element method for reaction–convection–diffusion equations Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240430
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan PryerThis paper introduces a novel approach to approximate a broad range of reaction–convection–diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the underlying differential equation. The main result of this work demonstrates that the numerical solution achieves an accuracy of O(hk) in the energy norm, where k represents

Exponential convergence to steadystates for trajectories of a damped dynamical system modeling adhesive strings Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240420
Giuseppe Maria Coclite, Nicola De Nitti, Francesco Maddalena, Gianluca Orlando, Enrique ZuazuaWe study the global wellposedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a onedimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points

Derivation and analysis of a nonlocal Hele–Shaw–Cahn–Hilliard system for flow in thin heterogeneous layers Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240413
Giuseppe Cardone, Willi Jäger, Jean Louis WoukengWe derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele–Shaw equation with memory coupled with the convective Cahn–Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its wellposedness in dimension 2. To achieve our goal, we develop and use the new concept of sigmaconvergence in thin heterogeneous

Asymptotic analysis of thin structures with pointdependent energy growth Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240413
Michela Eleuteri, Francesca Prinari, Elvira ZappaleIn this paper, 3D–2Ddimensional reduction for hyperelastic thin films modeled through energies with pointdependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of Γconvergence. Integral representation results, with a more regular Lagrangian related to the original energy density, are provided for the lower dimensional limiting energy, in different

Epidemics and society — A multiscale vision from the small world to the globally interconnected world Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240410
Diletta Burini, Damian A. KnopoffThis paper shows how a new theory of epidemics can be developed for viral pandemics in a globally interconnected world. The study of the inhost dynamics and, in parallel, the spatial diffusion of epidemics defines the goal of our work, which looks ahead to new mathematical tools to model epidemics beyond the traditional approach of population dynamics. The approach takes into account the evolutionary

The particle paths of hyperbolic conservation laws Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240403
Ulrik S. Fjordholm, Ola H. Mæhlen, Magnus C. ØrkeNonlinear scalar conservation laws are traditionally viewed as transport equations. We take instead the viewpoint of these PDEs as continuity equations with an implicitly defined velocity field. We show that a weak solution is the entropy solution if and only if the ODE corresponding to its velocity field is wellposed. We also show that the flow of the ODE is 1/2Hölder regular. Finally, we give several

Reaction–diffusion systems derived from kinetic theory for Multiple Sclerosis Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240328
João Miguel Oliveira, Romina TravagliniIn this paper, we present a mathematical study for the development of Multiple Sclerosis in which a spatiotemporal kinetic theory model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both interactions among different populations of human cells and the motion of immune cells, stimulated by cytokines. Moreover, we reproduce the consumption of myelin

Analysis of a spatiotemporal advectiondiffusion model for human behaviors during a catastrophic event Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240326
Kamal Khalil, Valentina Lanza, David Manceau, M. A. AzizAlaoui, Damienne ProvitoloIn this work, using the theory of firstorder macroscopic crowd models, we introduce a compartmental advection–diffusion model, describing the spatiotemporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and L1boundedness

Weak solutions to the heat conducting compressible selfgravitating flows in timedependent domains Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240325
Kuntal Bhandari, Bingkang Huang, Šárka NečasováIn this paper, we consider the heatconducting compressible selfgravitating fluids in timedependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill the fullslip boundary condition and the temperature on the boundary is given by a nonhomogeneous Dirichlet condition

Development of boundary layers in Euler fluids that on “activation” respond like Navier–Stokes fluids Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240325
P. A. GazcaOrozco, J. Málek, K. R. RajagopalWe consider the flow of a fluid whose response characteristics change due the value of the norm of the symmetric part of the velocity gradient, behaving as an Euler fluid below a critical value and as a Navier–Stokes fluid at and above the critical value, the norm being determined by the external stimuli. We show that such a fluid, while flowing past a bluff body, develops boundary layers which are

Global solvability of a twospecies chemotaxis–fluid system with Lotka–Volterra type competitive kinetics Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240319
Guoqiang Ren, Bin LiuIn this paper, we study a twospecies chemotaxis–fluid system with Lotka–Volterra type competitive kinetics in a bounded and smooth domain Ω⊂ℝ3 with noflux/Dirichlet boundary conditions. We present the global existence of weak energy solution to a twospecies chemotaxis Navier–Stokes system, and then the global weak energy solution which coincides with a smooth function throughout Ω¯×Π, where Π represents

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 3.6) Pub Date : 20240316
José García Otero, Mariusz Bodzioch, Juan BelmonteBeitiaCelyvir 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

Pedestrian models with congestion effects Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240315
Pedro AcevesSánchez, Rafael Bailo, Pierre Degond, Zoé MercierWe 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 semiimplicit, structurepreserving, and asymptoticpreserving numerical scheme which can handle the numerical solution

Macroscopic modeling of social crowds Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240315
Livio Gibelli, Damián A. Knopoff, Jie Liao, Wenbin YanSocial 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

Active particle methods towards a mathematics of living systems Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240313
Nicola Bellomo, Franco BrezziThis 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

Moment methods for kinetic traffic flow and a class of macroscopic traffic models Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240306
Raul Borsche, Axel KlarStarting from a nonlocal version of a classical kinetic traffic model, we derive a class of secondorder 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

Timediscrete momentum consensusbased optimization algorithm and its application to Lyapunov function approximation Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240305
SeungYeal Ha, Gyuyoung Hwang, Sungyoon KimIn this paper, we study a discrete momentum consensusbased optimization (MomentumCBO) algorithm which corresponds to a secondorder generalization of the discrete firstorder CBO [S.Y. Ha, S. Jin and D. Kim, Convergence of a firstorder consensusbased global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification

The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240305
Helmut Harbrecht, Marc Schmidlin, Christoph SchwabThis 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 sGevrey assumptions on the residual equation, we establish sGevrey bounds on the Fréchet derivatives of the locally

Predictioncorrection pedestrian flow by means of minimum flow problem Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240229
Hamza Ennaji, Noureddine Igbida, Ghadir JradiWe study a new variant of mathematical predictioncorrection model for crowd motion. The prediction phase is handled by a transport equation where the vector field is computed via an eikonal equation ∥∇φ∥=f, with a positive continuous function f connected to the speed of the spontaneous travel. The correction phase is handled by a new version of the minimum flow problem. This model is flexible and

Kinetic theory of active particles meets auction theory Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240227
Carla Crucianelli, Juan Pablo Pinasco, Nicolas SaintierIn 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 firstprice auctions with two bidders. Then, we formally derive the corresponding kinetic equations which describe the evolution over time of the distribution of

Impact of a unilateral horizontal gene transfer on the evolutionary equilibria of a population Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240224
Alejandro Gárriz, Alexis Léculier, Sepideh MirrahimiHow 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

Kinetic compartmental models driven by opinion dynamics: Vaccine hesitancy and social influence Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240221
Andrea Bondesan, Giuseppe Toscani, Mattia ZanellaWe 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

Optimal error bounds on timesplitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240221
Weizhu Bao, Ying Ma, Chushan WangWe establish optimal error bounds on timesplitting methods for the nonlinear Schrödinger equation with low regularity potential and typical powertype nonlinearity f(ρ)=ρσ, where ρ:=ψ2 is the density with ψ the wave function and σ>0 the exponent of the nonlinearity. For the firstorder Lie–Trotter timesplitting method, optimal L2norm error bound is proved for L∞potential and σ>0, and optimal

Inf–sup stabilized Scott–Vogelius pairs on general shaperegular simplicial grids by Raviart–Thomas enrichment Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240220
Volker John, Xu Li, Christian Merdon, Hongxing RuiThis paper considers the discretization of the Stokes equations with Scott–Vogelius pairs of finite element spaces on arbitrary shaperegular 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

Entropybased convergence rates of greedy algorithms Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240216
Yuwen Li, Jonathan W. SiegelWe 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 nwidths and enables us to obtain direct

A particle method for nonlocal advection–selection–mutation equations Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240214
Frank Ernesto Alvarez, Jules GuilberteauThe wellposedness of a nonlocal 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

An analysis of nonconforming virtual element methods on polytopal meshes with small faces Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240209
Hyeokjoo Park, Do Y. KwakIn this paper, we analyze nonconforming virtual element methods on polytopal meshes with small faces for the secondorder 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 L2inner product of certain projections on the

Derivation of effective theories for thin 3D nonlinearly elastic rods with voids Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240209
Manuel Friedrich, Leonard Kreutz, Konstantinos ZemasWe derive a dimensionreduction limit for a threedimensional rod with material voids by means of Γconvergence. Hereby, we generalize the results of the purely elastic setting [M. G. Mora and S. Müller, Derivation of the nonlinear bendingtorsion theory for inextensible rods by Γconvergence, Calc. Var. Partial Differential Equations 18 (2003) 287–305] to a framework of free discontinuity problems

Coupling the Navier–Stokes–Fourier equations with the Johnson–Segalman stressdiffusive viscoelastic model: Globalintime and largedata analysis Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240119
Michal Bathory, Miroslav Bulíček, Josef MálekWe prove that there exists a largedata and globalintime weak solution to a system of partial differential equations describing the unsteady flow of an incompressible heatconducting ratetype viscoelastic stressdiffusive fluid filling up a mechanically and thermally isolated container of any dimension. To overcome the principal difficulties connected with illposedness of the diffusive OldroydB

Korn–Maxwell–Sobolev inequalities for general incompatibilities Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240115
Franz Gmeineder, Peter Lewintan, Patrizio NeffWe establish a family of coercive Korntype inequalities for generalized incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the existence theory for a multitude of models in continuum mechanics in an optimal way. Different from our preceding work [F. Gmeineder, P. Lewintan and P. Neff, Optimal

Inexpensive polynomialdegreerobust equilibrated flux a posteriori estimates for isogeometric analysis Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20240110
Gregor Gantner, Martin VohralíkIn this paper, we consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e. vectorvalued mapped piecewise polynomials lying in the H(div) space which appropriately approximate the desired divergence constraint. Our estimates are constantfree in the

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 3.6) Pub Date : 20230802
Renhai Wang, Boling Guo, Daiwen HuangWe 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

A IETIDP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230802
Monica Montardini, Giancarlo Sangalli, Rainer Schneckenleitner, Stefan Takacs, Mattia TaniWe construct solvers for an isogeometric multipatch 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 DualPrimal IsogEometric Tearing and Interconnecting (IETIDP) method. We are interested in solving the arising patchlocal problems

Conforming and nonconforming virtual element methods for fourth order nonlocal reaction diffusion equation Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230724
Dibyendu Adak, Verónica Anaya, Mostafa Bendahmane, David MoraIn this work, we have designed conforming and nonconforming virtual element methods (VEM) to approximate nonstationary 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 wellposedness of the fully discrete scheme is derived. Further

Asymptotic behavior of a threedimensional haptotactic crossdiffusion system modeling oncolytic virotherapy Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230722
Yifu Wang, Chi XuThis paper deals with an initialboundary value problem for a doubly haptotactic crossdiffusion 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 selfmap argument, it is shown that under the assumption βmax{1,∥u0∥L∞(Ω)}<1+(1+1minx∈Ωu0(x))−1, this problem possesses

Regular solutions of chemotaxisconsumption systems involving tensorvalued sensitivities and Robin type boundary conditions Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230722
Jaewook Ahn, Kyungkeun Kang, Jihoon LeeThis paper deals with a parabolic–elliptic chemotaxisconsumption system with tensorvalued sensitivity S(x,n,c) under noflux boundary conditions for n and Robintype boundary conditions for c. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensorvalued sensitivity S. One of the main steps is to show that ∇c(⋅,t) becomes tiny in L2(Br(x)∩Ω)

Global classical solvability and stabilization in a twodimensional chemotaxis–fluid system with sublogarithmic sensitivity Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230720
Ji LiuIn 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 noflux/noflux/Dirichlet initialboundary value problem is globally solvable in the classical sense, and that if κ=0

Analysis of complex chemotaxis models Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230714
Youshan Tao, Michael WinklerThis 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.

Existence of multispikes in the Keller–Segel model with logistic growth Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230714
Fanze Kong, Juncheng Wei, Liangshun XuThe Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of unicellular and multicellular 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 multispiky solutions to the

Critical mass for Keller–Segel systems with supercritical nonlinear sensitivity Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230714
Xuan Mao, Yuxiang LiThis 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:x2n. 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)

Compressible Euler–Maxwell limit for global smooth solutions to the Vlasov–Maxwell–Boltzmann system Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230706
Renjun Duan, Dongcheng Yang, Hongjun YuTwo 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 selfconsistent electromagnetic interactions at the kinetic and fluid levels, respectively. It has remained a longstanding open problem to rigorously justify the hydrodynamic limit from the former to the latter

Global boundedness in a 2D chemotaxisNavier–Stokes system with flux limitation and nonlinear production Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230706
Wei WangWe consider the chemotaxisNavier–Stokes system with gradientdependent flux limitation and nonlinear production: nt+u⋅∇n=Δn−∇⋅(nf(∇c2)∇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.

Threespecies driftdiffusion models for memristors Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230629
Clément Jourdana, Ansgar Jüngel, Nicola ZamponiA system of driftdiffusion 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

An effective model for boundary vortices in thinfilm micromagnetics Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230621
Radu Ignat, Matthias KurzkeFerromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unitlength threedimensional 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

Human behavioral crowds review, critical analysis and research perspectives Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230606
Nicola Bellomo, Jie Liao, Annalisa Quaini, Lucia Russo, Constantinos SiettosThis 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

Crossdiffusion models in complex frameworks from microscopic to macroscopic Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230606
D. Burini, N. ChouhadThis 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 socalled 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

Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multipatch domains Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230531
Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael VázquezIsogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensorproduct structure of standard multivariate Bspline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multipatch geometries

Singular patterns in Keller–Segeltype models Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230529
Juan Campos, Carlos Pulido, Juan Soler, Mario VerueteThe aim of this paper is to elucidate the existence of patterns for Keller–Segeltype 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 socalled nonlinear diffusion through saturated flux mechanisms for the movement cell. At the same time, we analyze various transport operators

Multigrid solvers for isogeometric discretizations of the second biharmonic problem Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230529
Jarle Sogn, Stefan TakacsWe develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zeroorder 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

Nonisothermal nonNewtonian fluids: The stationary case Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230525
Maurizio Grasselli, Nicola Parolini, Andrea Poiatti, Marco VeraniThe stationary Navier–Stokes equations for a nonNewtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlettype 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

Numerical modeling of the brain poromechanics by highorder discontinuous Galerkin methods Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230520
Mattia Corti, Paola F. Antonietti, Luca Dede’, Alfio M. QuarteroniWe introduce and analyze a discontinuous Galerkin method for the numerical modeling of the equations of MultipleNetwork 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 highorder discontinuous Galerkin method on polygonal and polyhedral

Boundedness and large time behavior of solutions of a higherdimensional haptotactic system modeling oncolytic virotherapy Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230520
Jiashan Zheng, Yuanyuan KeThis paper is concerned with the higherdimensional 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 crossdiffusion models in complex environments: Models and analytic problems toward

Analysis of a fullydiscrete, nonconforming approximation of evolution equations and applications Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230517
A. Kaltenbach, M. RůžičkaIn this paper, we consider a fullydiscrete approximation of an abstract evolution equation deploying a nonconforming 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

Lack of robustness and accuracy of many numerical schemes for phasefield simulations Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230516
Jinchao Xu, Xiaofeng XuIn this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phasefield 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 firstorder fully implicit scheme is the

Variational multiscale method stabilization parameter calculated from the strainrate tensor Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230515
Kenji Takizawa, Yuto Otoguro, Tayfun E. TezduyarThe stabilization parameters of the methods like the StreamlineUpwind/Petrov–Galerkin, PressureStabilizing/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

L1Theory for HeleShaw flow with linear drift Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230511
Noureddine IgbidaThe main goal of this paper is to prove L1comparison and contraction principles for weak solutions of PDE system corresponding to a phase transition diffusion model of HeleShaw 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

The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230510
Patrick HenningIn 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

A nonlinear bending theory for nematic LCE plates Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230504
Sören Bartels, Max Griehl, Stefan Neukamm, David PadillaGarza, Christian PalusIn 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 stressfree 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 nonflat deformations

Collective behaviors of stochastic agentbased models and applications to finance and optimization Math. Models Methods Appl. Sci. (IF 3.6) Pub Date : 20230426
Dongnam Ko, SeungYeal Ha, Euntaek Lee, Woojoo ShimIn 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