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Global well-posedness of a conservative relaxed cross diffusion system.

Thomas Lepoutre 1, 2 Michel Pierre 3 Guillaume Rolland 3 
1 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]
Abstract : We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form $u_i\to \partial_tu_i-\Delta(a_i(\tilde{u})u_i)$ where the $u_i, i=1,...,I$ represent $I$ density-functions, $\tilde{u}$ is a spatially regularized form of $(u_1,...,u_I)$ and the nonlinearities $a_i$ are merely assumed to be continuous and bounded from below. Existence of global weak solutions is obtained in any space dimension. Solutions are proved to be regular and unique when the $a_i$ are locally Lipschitz continuous.
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https://hal.inria.fr/hal-00683006
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Submitted on : Tuesday, March 27, 2012 - 2:59:51 PM
Last modification on : Friday, May 20, 2022 - 9:04:46 AM
Long-term archiving on: : Thursday, June 28, 2012 - 2:30:38 AM

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Thomas Lepoutre, Michel Pierre, Guillaume Rolland. Global well-posedness of a conservative relaxed cross diffusion system.. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2012, 44 (3), pp.1674-1693. ⟨10.1137/110848839⟩. ⟨hal-00683006⟩

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