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A multiscale colloid transport model with anistropic degenerate diffusion

Abstract : We consider a weakly coupled semilinear parabolic-hyperbolic system with a degenerate and anisotropic diffusion. It arises to model the evolution of a chemical or biological tracer in a porous medium. We study the well-posed- ness of the system using a L^1 theory. Then, we establish the relaxation limit as the reaction constant becomes large. We prove that the system converges to a nonlinear parabolic-hyperbolic equation that generalizes the Stefan problem. Two specificities of this paper are (i) to deal with ill-prepared initial data and (ii) with unique entropy solutions based on a precise entropy inequality.
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https://hal.inria.fr/hal-00694622
Contributor : Jean-Frédéric Gerbeau <>
Submitted on : Saturday, May 5, 2012 - 9:41:52 AM
Last modification on : Tuesday, November 17, 2020 - 10:26:08 AM

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  • HAL Id : hal-00694622, version 1

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Mohamed Belhadj, Jean-Frédéric Gerbeau, Benoît Perthame. A multiscale colloid transport model with anistropic degenerate diffusion. Asymptotic Analysis, IOS Press, 2003, 34 (1), pp.41-54. ⟨hal-00694622⟩

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