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

Noemi David; Tomasz Dębiec; Benoît Perthame

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arXiv · 2108.00787

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

Noemi David·Tomasz Dębiec·Benoît Perthame

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Abstract

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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Noemi David, Tomasz Dębiec, Benoît Perthame. 2021-08-02. Convergence rate for the incompressible limit of nonlinear diffusion-advection equations. https://arxiv.org/abs/2108.00787

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