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Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-02-27 Tommaso Lorenzi, Fiona R. Macfarlane, Kevin J. Painter
We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from ‘fully mesenchymal’ to ‘fully epithelial’. The more mesenchymal cells are those that display stronger haptotaxis responses and have greater capacity to modify the extracellular matrix (ECM) through enhanced secretion of matrix-degrading enzymes (MDEs)
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A data-driven kinetic model for opinion dynamics with social network contacts Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-02-20 Giacomo Albi, Elisa Calzola, Giacomo Dimarco
Opinion dynamics is an important and very active area of research that delves into the complex processes through which individuals form and modify their opinions within a social context. The ability to comprehend and unravel the mechanisms that drive opinion formation is of great significance for predicting a wide range of social phenomena such as political polarisation, the diffusion of misinformation
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The turnpike property for mean-field optimal control problems Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-02-12 Martin Gugat, Michael Herty, Chiara Segala
We study the turnpike phenomenon for optimal control problems with mean-field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the optimal control problems with large time horizons give rise to a turnpike structure of the optimal state and the optimal control. For the proof, we use the fact that
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From NeurODEs to AutoencODEs: A mean-field control framework for width-varying neural networks Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-02-08 Cristina Cipriani, Massimo Fornasier, Alessandro Scagliotti
The connection between Residual Neural Networks (ResNets) and continuous-time control systems (known as NeurODEs) has led to a mathematical analysis of neural networks, which has provided interesting results of both theoretical and practical significance. However, by construction, NeurODEs have been limited to describing constant-width layers, making them unsuitable for modelling deep learning architectures
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Network-based kinetic models: Emergence of a statistical description of the graph topology Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-02-02 Marco Nurisso, Matteo Raviola, Andrea Tosin
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interactions a statistical description of the graph topology, given in terms of the degree distribution embedded in a Boltzmann-type kinetic equation, is
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The dynamical analysis of a nonlocal predator–prey model with cannibalism Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-01-29 Daifeng Duan, Ben Niu, Junjie Wei, Yuan Yuan
Cannibalism is often an extreme interaction in the animal species to quell competition for limited resources. To model this critical factor, we improve the predator–prey model with nonlocal competition effect by incorporating the cannibalism term, and different kernels for competition are considered in this model numerically. We give the critical conditions leading to the double Hopf bifurcation, in
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Global dynamics and spatiotemporal heterogeneity of a preytaxis model with prey-induced acceleration Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-01-26 Chunlai Mu, Weirun Tao, Zhi-An Wang
Conventional preytaxis systems assume that prey-tactic velocity is proportional to the prey density gradient. However, many experiments exploring the predator–prey interactions show that it is the predator’s acceleration instead of velocity that is proportional to the prey density gradient in the prey-tactic movement, which we call preytaxis with prey-induced acceleration. Mathematical models of preytaxis
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On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-01-25 Rachidi B. Salako, Yixiang Wu
In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the susceptible or infected people to zero and study the corresponding degenerate reaction-diffusion model. Our main approach to study the global dynamics of these models is to
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The fully parabolic multi-species chemotaxis system in Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-01-19 Ke Lin
This article is devoted to the analysis of the parabolic–parabolic chemotaxis system with multi-components over $\mathbb{R}^2$ . The optimal small initial condition on the global existence of solutions for multi-species chemotaxis model in the fully parabolic situation had not been attained as far as the author knows. In this paper, we prove that under the sub-critical mass condition, any solutions
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Recurrent and chaotic outbreaks in SIR model Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-01-18 Chunyi Gai, Theodore Kolokolnikov, Jan Schrader, Vedant Sharma
We examine several extensions to the basic Susceptible-Infected-Recovered model, which are able to induce recurrent outbreaks (the basic Susceptible-Infected-Recovered model by itself does not exhibit recurrent outbreaks). We first analyse how slow seasonal variations can destabilise the endemic equilibrium, leading to recurrent outbreaks. In the limit of slow immunity loss, we derive asymptotic thresholds
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Absolute concentration robustness and multistationarity in reaction networks: Conditions for coexistence Eur. J. Appl. Math. (IF 1.9) Pub Date : 2024-01-02 Nidhi Kaihnsa, Tung Nguyen, Anne Shiu
Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state, while some networks exhibit absolute concentration robustness (ACR), which means that some species concentration is the same at all steady states. Both multistationarity and ACR are significant in biological settings, but only recently has attention focused on the possibility
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Variational inequalities arising from credit rating migration with buffer zone Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-12-14 Xinfu Chen, Jin Liang
In Chen and Liang previous work, a model, together with its well-posedness, was established for credit rating migrations with different upgrade and downgrade thresholds (i.e. a buffer zone, also called dead band in engineering). When positive dividends are introduced, the model in Chen and Liang (SIAM Financ. Math. 12, 941–966, 2021) may not be well-posed. Here, in this paper, a new model is proposed
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Analysis and numerical simulations of travelling waves due to plant–soil negative feedback Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-12-07 Annalisa Iuorio, Nicole Salvatori, Gerardo Toraldo, Francesco Giannino
In this work, we carry out an analytical and numerical investigation of travelling waves representing arced vegetation patterns on sloped terrains. These patterns are reported to appear also in ecosystems which are not water deprived; therefore, we study the hypothesis that their appearance is due to plant–soil negative feedback, namely due to biomass-(auto)toxicity interactions. To this aim, we introduce
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Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-12-04 Juan He, Guo-Bao Zhang, Ting Liu
This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed $c^*$ , the existence of travelling wavefronts with the wave speed $c\ge c^*$ and the nonexistence of travelling
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Leveraging memory effects and gradient information in consensus-based optimisation: On global convergence in mean-field law Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-10-20 Konstantin Riedl
In this paper, we study consensus-based optimisation (CBO), a versatile, flexible and customisable optimisation method suitable for performing nonconvex and nonsmooth global optimisations in high dimensions. CBO is a multi-particle metaheuristic, which is effective in various applications and at the same time amenable to theoretical analysis thanks to its minimalistic design. The underlying dynamics
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Effects of concurrency on epidemic spreading in Markovian temporal networks Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-10-18 Ruodan Liu, Masaki Ogura, Elohim Fonseca Dos Reis, Naoki Masuda
The concurrency of edges, quantified by the number of edges that share a common node at a given time point, may be an important determinant of epidemic processes in temporal networks. We propose theoretically tractable Markovian temporal network models in which each edge flips between the active and inactive states in continuous time. The different models have different amounts of concurrency while
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Sharp asymptotic profile of the solution to a West Nile virus model with free boundary Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-10-13 Zhiguo Wang, Hua Nie, Yihong Du
We consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval $[g(t), h(t)]$ in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and
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Generalised solution to a 2D parabolic-parabolic chemotaxis system for urban crime: Global existence and large-time behaviour Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-09-25 Bin Li, Li Xie
We consider a parabolic-parabolic chemotaxis system with singular chemotactic sensitivity and source functions, which is originally introduced by Short et al to model the spatio-temporal behaviour of urban criminal activities with the particular value of the chemotactic sensitivity parameter $\chi =2$ . The available analytical findings for this urban crime model including $\chi =2$ are restricted
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Steady-state solutions for a reaction–diffusion equation with Robin boundary conditions: Application to the control of dengue vectors Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-09-18 Luis Almeida, Pierre-Alexandre Bliman, Nga Nguyen, Nicolas Vauchelet
In this paper, we investigate an initial-boundary value problem of a reaction–diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary. This problem arises in the study of mosquito populations under the intervention of the population replacement method, where the boundary condition takes into account
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Breakdown of electroneutrality in polyelectrolyte gels Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-09-06 Matthew G. Hennessy, Giulia L. Celora, Sarah L. Waters, Andreas Münch, Barbara Wagner
Mathematical models of polyelectrolyte gels are often simplified by assuming the gel is electrically neutral. The rationale behind this assumption is that the thickness of the electric double layer (EDL) at the free surface of the gel is small compared to the size of the gel. Hence, the thin-EDL limit is taken, in which the thickness of the EDL is set to zero. Despite the widespread use of the thin-EDL
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A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-08-31 Bruno Carbonaro, Marco Menale
The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the ‘forcing term’. Firstly, the interactions between pairs of particles are both conservative and
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Spreading dynamics of a diffusive epidemic model with free boundaries and two delays Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-08-11 Qiaoling Chen, Sanyi Tang, Zhidong Teng, Feng Wang
A delayed reaction-diffusion system with free boundaries is investigated in this paper to understand how the bacteria spread spatially to larger area from the initial infected habitat. Under the assumptions that the nonlinearities are of monostable type and the initial values satisfy some compatible condition, we show that the free boundary problem is well-posed and discuss the long-time behaviour
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Characterising small objects in the regime between the eddy current model and wave propagation Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-08-08 Paul David Ledger, William R. B. Lionheart
Being able to characterise objects at low frequencies, but in situations where the modelling error in the eddy current approximation of the Maxwell system becomes large, is important for improving current metal detection technologies. Importantly, the modelling error becomes large as the frequency increases, but the accuracy of the eddy current model also depends on the object topology and on its materials
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The effect of pore-scale contaminant distribution on the reactive decontamination of porous media Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-08-08 Ellen K. Luckins, Christopher J. W. Breward, Ian M. Griffiths, Colin P. Please
A porous material that has been contaminated with a hazardous chemical agent is typically decontaminated by applying a cleanser solution to the surface and allowing the cleanser to react into the porous material, neutralising the agent. The agent and cleanser are often immiscible fluids and so, if the porous material is initially saturated with agent, a reaction front develops with the decontamination
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Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-07-18 Zhomart Turarov, Claudia Totzeck
We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces (Totzeck (2020) Kinet. Relat. Models 13(6), 1219–1242.) by including the agents’ body size. The influence of the body size on the self-organisation of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model
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Dynamics and steady state of squirmer motion in liquid crystal Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-07-10 Leonid Berlyand, Hai Chi, Mykhailo Potomkin, Nung Kwan Yip
We analyse a nonlinear partial differential equation system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer’s motility, the squirmer model is used in which self-propulsion enters the model through the slip velocity on the microswimmer’s surface. The liquid crystal is described using the well-established Beris–Edwards formulation. In previous computational
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Instability of axisymmetric flow in thermocapillary liquid bridges: Kinetic and thermal energy budgets for two-phase flow with temperature-dependent material properties Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-07-07 Mario Stojanović, Francesco Romanò, Hendrik C. Kuhlmann
In numerical linear stability investigations, the rates of change of the kinetic and thermal energy of the perturbation flow are often used to identify the dominant mechanisms by which kinetic or thermal energy is exchanged between the basic and the perturbation flow. Extending the conventional energy analysis for a single-phase Boussinesq fluid, the energy budgets of arbitrary infinitesimal perturbations
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Local existence of strong solutions to micro–macro models for reactive transport in evolving porous media Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-06-19 Stephan Gärttner, Peter Knabner, Nadja Ray
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenised flow and transport equations are solved on the macroscopic scale, while effective parameters are obtained from auxiliary cell problems on possibly evolving reference geometries (micro-scale). Despite their perspective success in rendering lab/field-scale simulations
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Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-06-14 John R. King, Giles W. Richardson, Jamie M. Foster
The dynamics of interfaces in slow diffusion equations with strong absorption are studied. Asymptotic methods are used to give descriptions of the behaviour local to a comprehensive range of possible singular events that can occur in any evolution. These events are: when an interface changes its direction of propagation (reversing and anti-reversing), when an interface detaches from an absorbing obstacle
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Resilience of dynamical systems Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-06-05 Hana Krakovská, Christian Kuehn, Iacopo P. Longo
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining the ‘global stability’ of a nonlinear system is very challenging. Over the last few decades, many different ideas have been developed to address this issue, primarily driven by concrete applications. In particular, several disciplines suggested a web of concepts under the headline
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-coupling mechanisms are sufficient to obtain exponential decay in strain gradient elasticity Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-05-22 Jose R. Fernández, Ramón Quintanilla
In this paper, we consider the time decay of the solutions to some problems arising in strain gradient thermoelasticity. We restrict to the two-dimensional case, and we assume that two dissipative mechanisms are introduced, the temperature and the mass dissipation. First, we show that this problem is well-posed proving that the operator defining it generates a contractive semigroup of linear operators
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On a class of nonlocal continuity equations on graphs Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-05-17 Antonio Esposito, Francesco Saverio Patacchini, André Schlichting
Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We consider general interpolation functions, which give rise to a variety of different dynamics, for example, the nonlocal interaction dynamics coming from a solution-dependent
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Extended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equation Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-05-05 Serhii D. Koval, Alexander Bihlo, Roman O. Popovych
We carry out the extended symmetry analysis of an ultraparabolic Fokker–Planck equation with three independent variables, which is also called the Kolmogorov equation and is singled out within the class of such Fokker–Planck equations by its remarkable symmetry properties. In particular, its essential Lie invariance algebra is eight-dimensional, which is the maximum dimension within the above class
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Positive solutions to the prey–predator equations with dormancy of predators Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-04-24 Novrianti, Okihiro Sawada, Naoki Tsuge
The time-global unique classical positive solutions to the reaction–diffusion equations for prey–predator models with dormancy of predators are constructed. The feature appears on the nonlinear terms of Holling type $\rm I\!I$ functional response. The crucial step is to establish time-local positive classical solutions by using a new approximation associated with time-evolution operators. Although
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Increasing stability for the inverse source problem in elastic waves with attenuation Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-04-20 Ganghua Yuan, Yue Zhao
This paper is concerned with the increasing stability of the inverse source problem for the elastic wave equation with attenuation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The stability also shows exponential dependence on the
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Time-dependent modelling of thin poroelastic films drying on deformable plates Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-04-12 Matthew G. Hennessy, Richard V. Craster, Omar K. Matar
Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the film during drying are transmitted to the plate and
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On macrosegregation in a binary alloy undergoing solidification shrinkage Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-03-23 Milton Assunção, Michael Vynnycky
The one-dimensional transient solidification of a binary alloy undergoing shrinkage is well-known as an invaluable benchmark for the testing of numerical codes that model macrosegregation. Here, recent work that considered the small-time behaviour of this problem is extended until complete solidification, thereby determining the solute profile across the entire solidified domain. The small-time solution
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Dynamics of a delayed population patch model with the dispersion matrix incorporating population loss Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-03-21 Dan Huang, Shanshan Chen
In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate is smaller than a critical value. The stability of the positive equilibrium and associated Hopf bifurcation are investigated when the dispersal rate is small or
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Partial Euler operators and the efficient inversion of Div Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-03-20 P. E. Hydon
The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems have conservation laws of arbitrarily high order that must be found with the aid of computer algebra. Even low-order conservation laws of complex systems can be
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Dimension reduction analysis of a three-dimensional thin elastic plate reinforced with fractal ribbons Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-03-02 Mustapha El Jarroudi, Mhamed El Merzguioui, Mustapha Er-Riani, Aadil Lahrouz, Jamal El Amrani
The aim of this paper is to study the dimension reduction analysis of an elastic plate with small thickness reinforced with increasing number of thin ribbons developing fractal geometry. We prove the $\Gamma $ -convergence of the energy functionals to a two-dimensional effective energy including singular terms supported within the Sierpinski carpet.
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Constrained exact boundary controllability of a semilinear model for pipeline gas flow Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-02-01 Martin Gugat, Jens Habermann, Michael Hintermüller, Olivier Huber
While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures
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A homogenised model for the motion of evaporating fronts in porous media Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-01-23 Ellen K. Luckins, Christopher J. W. Breward, Ian M. Griffiths, Colin P. Please
Evaporation within porous media is both a multiscale and interface-driven process, since the phase change at the evaporating interfaces within the pores generates a vapour flow and depends on the transport of vapour through the porous medium. While homogenised models of flow and chemical transport in porous media allow multiscale processes to be modelled efficiently, it is not clear how the multiscale
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Battleship, tomography and quantum annealing Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-01-16 W. Riley Casper, Taylor Grimes
The classic game of Battleship involves two players taking turns attempting to guess the positions of a fleet of vertically or horizontally positioned enemy ships hidden on a $10\times 10$ grid. One variant of this game, also referred to as Battleship Solitaire, Bimaru or Yubotu, considers the game with the inclusion of X-ray data, represented by knowledge of how many spots are occupied in each row
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Solving two-dimensional H(curl)-elliptic interface systems with optimal convergence on unfitted meshes Eur. J. Appl. Math. (IF 1.9) Pub Date : 2023-01-05 Ruchi Guo, Yanping Lin, Jun Zou
Finite element methods developed for unfitted meshes have been widely applied to various interface problems. However, many of them resort to non-conforming spaces for approximation, which is a critical obstacle for the extension to $\textbf{H}(\text{curl})$ equations. This essential issue stems from the underlying Sobolev space $\textbf{H}^s(\text{curl};\,\Omega)$ , and even the widely used penalty
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Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-12-16 Mahmood R. Tarayrah, Brian Pitzel, Alexei Cheviakov
The frameworks of Baikov–Gazizov–Ibragimov (BGI) and Fushchich–Shtelen (FS) approximate symmetries are used to study symmetry properties of partial differential equations with a small parameter. In general, it is shown that unlike the case of ordinary differential equations (ODEs), unstable BGI point symmetries of unperturbed partial differential equations (PDEs) do not necessarily yield local approximate
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Constant rank factorisations of smooth maps, with applications to sonar Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-12-01 Michael Robinson
Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object’s shape and composition. Traditional synthetic aperture processing is highly effective in solving classification problems when the conditions are favourable but relies on accurate knowledge of the sensor’s trajectory relative to the object being measured
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A modelling framework for efficient reduced order simulations of parametrised lithium-ion battery cells Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-11-29 M. Landstorfer, M. Ohlberger, S. Rave, M. Tacke
In this contribution, we present a modelling and simulation framework for parametrised lithium-ion battery cells. We first derive a continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterised non-linear system of partial differential equations, the reduced basis method is employed. The reduced
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Global optimisation of the mean first passage time for narrow capture problems in elliptic domains Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-11-28 Jason Gilbert, Alexei Cheviakov
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known how the escape time decreases with the increase of the trap sizes, for some specific 2D and 3D domains, higher-order asymptotic formulas have been established, providing
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Exact nonclassical symmetry solutions of Lotka–Volterra-type population systems Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-11-25 P. Broadbridge, R. M. Cherniha, J. M. Goard
New classes of conditionally integrable systems of nonlinear reaction–diffusion equations are introduced. They are obtained by extending a well-known nonclassical symmetry of a scalar partial differential equation to a vector equation. New exact solutions of nonlinear predator–prey systems with cross-diffusion are constructed. Infinite dimensional classes of exact solutions are made available for such
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Symmetry actions and brackets for adjoint-symmetries. II: Physical examples Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-11-21 Stephen C. Anco
Symmetries and adjoint-symmetries are two fundamental (coordinate-free) structures of PDE systems. Recent work has developed several new algebraic aspects of adjoint-symmetries: three fundamental actions of symmetries on adjoint-symmetries; a Lie bracket on the set of adjoint-symmetries given by the range of a symmetry action; a generalised Noether (pre-symplectic) operator constructed from any non-variational
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Existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-11-11 MIN GAO, MATTHIAS WINTER, WEN YANG
In this paper, we consider the existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field. We prove the existence of three types of singular steady-state patterns (double fronts, single spikes, and double spikes) by solving their respective consistency conditions. In the case of single spikes, we prove the stability of single small spike solution for sufficiently
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A deterministic gradient-based approach to avoid saddle points Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-11-09 L. M. Kreusser, S. J. Osher, B. Wang
Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed
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Symmetry actions and brackets for adjoint-symmetries. I: Main results and applications Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-10-19 Stephen C. Anco
Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions of the linearisation (Frechet derivative) equation holding on the space of solutions to the PDE, and they are well-known to comprise a linear space having the structure of a Lie algebra. Solutions of the adjoint linearisation equation holding on the space of solutions to the PDE are called
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Modelling, simulation and optimisation of parabolic trough power plants Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-10-11 H. BAKHTI, I. GASSER, S. SCHUSTER, E. PARFENOV
We present a mathematical model built to describe the fluid dynamics for the heat transfer fluid in a parabolic trough power plant. Such a power plant consists of a network of tubes for the heat transport fluid. In view of optimisation tasks in the planning and in the operational phase, it is crucial to find a compromise between a very detailed description of many possible physical phenomena and a
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Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-10-10 A. M. R. RADJEN, R. H. TEW, G. GRADONI
The standard approach to applying ray theory to solving Maxwell’s equations in the large wave-number limit involves seeking solutions that have (i) an oscillatory exponential with a phase term that is linear in the wave-number and (ii) has an amplitude profile expressed in terms of inverse powers of that wave-number. The Friedlander–Keller modification includes an additional power of this wave-number
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Projective invariants of images Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-09-26 PETER J. OLVER
The method of equivariant moving frames is employed to construct and completely classify the differential invariants for the action of the projective group on functions defined on the two-dimensional projective plane. While there are four independent differential invariants of order $\leq 3$, it is proved that the algebra of differential invariants is generated by just two of them through invariant
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Convergence to a self-similar solution for a one-phase Stefan problem arising in corrosion theory Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-08-09 M. BOUGUEZZI, D. HILHORST, Y. MIYAMOTO, J.-F. SCHEID
Steel corrosion plays a central role in different technological fields. In this article, we consider a simple case of a corrosion phenomenon which describes a pure iron dissolution in sodium chloride. This article is devoted to prove rigorously that under rather general hypotheses on the initial data, the solution of this iron dissolution model converges to a self-similar profile as $t\rightarrow +\infty$
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Impacts of noise on quenching of some models arising in MEMS technology Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-08-09 OURANIA DROSINOU, NIKOS I. KAVALLARIS, CHRISTOS V. NIKOLOPOULOS
In the current work, we study a stochastic parabolic problem. The presented problem is motivated by the study of an idealised electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of the potential difference, a parameter that actually controls the operation of MEMS device. We first present the construction of the mathematical model, and then, we deduce
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Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-07-25 Y. A. ANTIPOV, S. M. MKHITARYAN
Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterised by the Young modulus varying with depth as a power function. This paper models Hertzian and adhesive contact of two elastic inhomogeneous power-law graded bodies with different exponents. The problem is governed by an integral
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Profiling ponded soil surface in saturated seepage into drain-line sink: Kalashnikov’s method of lateral leaching revisited Eur. J. Appl. Math. (IF 1.9) Pub Date : 2022-07-12 A. R. KACIMOV, YU. V. OBNOSOV
Two boundary value problems are solved for potential steady-state 2D Darcian seepage flows towards a line sink in a homogeneous isotropic soil from a ponded land surface, which is not flat but profiled. The aim of this shaping is ‘uniformisation’ of the velocity and travel time between this surface and a horizontal drain modelled by a line sink. The complex potential domain is a half-strip, which is