Prof. Filomena Feo “The asymptotic behaviour for the solutions to ananisotropic diffusion equation in the slow and fast diffusion regime”

In this talk, we present some recent results concerning the nonnegative solutions of the following anisotropic equation
\sum_{i=1}^N (u^{m_i})_{x_ix_i} in R^N × (0, +∞)

with N ≥ 2 and m_i > 0 for i = 1,… , N. We focus on two distinct diffusion regimes: the slow (m_i > 1 for all i) and fast (m_i < 1 for all i) diffusion in all directions. We address, in particular, the existence and uniqueness of a self-similar fundamental solution and the asymptotic behavior of nonnegative solutions of the Cauchy problem with L^1 initial data.

Based on some recent joint papers with J. L. V ́azquez and B. Volzone.