| Abstract: |
| In this talk, we will present some recent results concerning the nonnegative solutions of the following anisotropic equation
\begin{equation*}\label{APM}
u_t=\sum_{i=1}^N(u^{m_i})_{x_i x_i}\quad\quad \mbox{in } \ \quad \mathbb{R}^N\times(0,+\infty)
\end{equation*}
with $N\geq2$ and $m_i>0$ for $i=1,...,N$. We focus on the slow ($m_i>1$ for all $i$) diffusion in all directions. We examine, 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. |
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