Year: 2012
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Lukkari, Teemu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1578650381