Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774052 | Journal of Differential Equations | 2017 | 36 Pages |
Abstract
We study the nonlinear diffusion equation ut=ÎÏ(u) on general Euclidean domains, with homogeneous Neumann boundary conditions. We assume that Ïâ²(u) is bounded from below by |u|m1â1 for small |u| and by |u|m2â1 for large |u|, the two exponents m1,m2 being possibly different and larger than one. The equality case corresponds to the well-known porous medium equation. We establish sharp short- and long-time Lq0-Lâ smoothing estimates: similar issues have widely been investigated in the literature in the last few years, but the Neumann problem with different powers had not been addressed yet. This work extends some previous results in many directions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Alin Razvan Fotache, Matteo Muratori,