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.
Cite this article
Noemi David, Tomasz Dębiec, Benoît Perthame, Convergence rate for the incompressible limit of nonlinear diffusion–advection equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 3, pp. 511–529DOI 10.4171/AIHPC/53