1 research outputs found
Smoothing effects for the filtration equation with different powers
We study the nonlinear diffusion equation on general
Euclidean domains, with homogeneous Neumann boundary conditions. We assume that
is bounded from below by for small
and by for large , the two exponents 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 - 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