Entropy, Duality and Cross Diffusion
Laurent Desvillettes, Thomas Lepoutre, Ayman Moussa
TL;DR
This paper explores the use of entropy and duality methods to establish the existence of solutions for reaction-cross diffusion systems involving two species, relevant in population dynamics with self and cross diffusion effects.
Contribution
It introduces a novel application of entropy and duality techniques to prove existence results for reaction-cross diffusion systems in any spatial dimension.
Findings
Established existence of solutions for reaction-cross diffusion systems
Applied entropy and duality methods to complex population models
Extended analysis to systems with cross diffusion in arbitrary dimensions
Abstract
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. Those systems appear in population dynamics when the diffusion rates of individuals of two species depend on the concentration of individuals of the same species (self-diffusion), or of the other species (cross diffusion).
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Mathematical Biology Tumor Growth