Stability of solutions to nonlinear diffusion equations

Abstract

We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit problem with the same data as $m$ varies. Our arguments are elementary and based on a general principle. We use neither regularity theory nor nonlinear semigroups, and our approach applies to e.g. Dirichlet problems in bounded domains and Cauchy problems on the whole space.

arXiv commentRevised introduction, some references added