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Article Dans Une Revue Annales de l'Institut Henri Poincaré C, Analyse non linéaire Année : 2022

Convergence rate for the incompressible limit of nonlinear diffusion–advection equations

Résumé

The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type. Although vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV-uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces.
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Dates et versions

hal-03912924 , version 1 (26-12-2022)

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Noemi David, Tomasz Dębiec, Benoît Perthame. Convergence rate for the incompressible limit of nonlinear diffusion–advection equations. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2022, ⟨10.4171/aihpc/53⟩. ⟨hal-03912924⟩
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