Convergence rate for the incompressible limit of nonlinear diffusion–advection equations
Noemi David, Tomasz Dębiec, Benoı̂t Perthame · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2022
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 cellpopulation models to free boundary problems of Hele–Shaw type. Although a 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.