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Entropy, Duality and Cross Diffusion

Laurent Desvillettes 1 Thomas Lepoutre 2, 3, 4 Ayman Moussa 5, 6 
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
4 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
6 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
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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https://hal.inria.fr/hal-00785379
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Submitted on : Wednesday, February 6, 2013 - 10:07:40 AM
Last modification on : Tuesday, November 15, 2022 - 3:52:44 PM

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Laurent Desvillettes, Thomas Lepoutre, Ayman Moussa. Entropy, Duality and Cross Diffusion. SIAM Journal on Mathematical Analysis, 2014, 46 (1), pp.820-853. ⟨10.1137/130908701⟩. ⟨hal-00785379⟩

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