arXiv:1206.2492 [math.AP]AbstractReferencesReviewsResources
Stability of solutions to nonlinear diffusion equations
Published 2012-06-12, updated 2013-09-03Version 3
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.
Comments: Revised introduction, some references added
Categories: math.AP
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