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Entropy, Duality and Cross Diffusion [PDF]
SIAM Journal on Mathematical Analysis, 2013 This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space.
Desvillettes, Laurent +2 more
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Cross-diffusion driven instability in a predator-prey system with cross-diffusion [PDF]
Acta Applicandae Mathematicae, 2014 In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics.
Lombardo, Maria Carmela +2 more
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Cross-diffusion systems with entropy structure [PDF]
SIAM Journal on Mathematical Analysis, 2017 Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems by Lepoutre ...
Jüngel, Ansgar
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Homogenization of degenerate cross-diffusion systems [PDF]
Journal of Differential Equations, 2018 Two-scale homogenization limits of parabolic cross-diffusion systems in a heterogeneous medium with no-flux boundary conditions are proved. The heterogeneity of the medium is reflected in the diffusion coefficients or by the perforated domain.
Juengel, Ansgar, Ptashnyk, Mariya
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Vanishing cross-diffusion limit in a Keller–Segel system with additional cross-diffusion [PDF]
Nonlinear Analysis, 2020 Keller-Segel systems in two and three space dimensions with an additional cross-diffusion term in the equation for the chemical concentration are analyzed. The cross-diffusion term has a stabilizing effect and leads to the global-in-time existence of weak solutions.
Jüngel, Ansgar +2 more
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Cross-Diffusion Modeling in Macroeconomics [PDF]
Differential Equations and Dynamical Systems, 2014 This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator-prey system in population-dynamics. The spatial movement of the capital and labour force are taken into account by cross-diffusion effect.
Balázsi, L., Kiss, Krisztina
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Global Existence for some Cross Diffusion Systems with Equal Cross Diffusion/Reaction Rates [PDF]
Advanced Nonlinear Studies, 2020 Abstract We consider some cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada–Kawasaki–Teramoto (SKT) model in population biology. We establish the global existence of strong solutions to systems for multiple species having equal either diffusion or reaction rates.
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Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces [PDF]
, 2014 The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces.
A. Madzvamuse +9 more
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Lie symmetries of the Shigesada-Kawasaki-Teramoto system [PDF]
, 2016 The Shigesada-Kawasaki-Teramoto system, which consists of two reaction-diffusion equations with variable cross-diffusion and quadratic nonlinearities, is considered.
Cherniha, Roman +2 more
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Rigorous mean-field limit and cross-diffusion [PDF]
Zeitschrift für angewandte Mathematik und Physik, 2019 The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations. The mean-field limit is performed in two steps: First, the many-particle system leads in the large population limit
Li Chen, Esther S. Daus, Ansgar Jüngel
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