The Degeneracy of a Fast-Diffusion Equation and Stability
Yuanwei Qi · SIAM Journal on Mathematical Analysis · 1996
It is known that for any nonnegative initial value $u_0 (x)$, the solution $u(x,t)$ of the initial-boundary value problem $u_t = {\operatorname{div}}(| abla u|^{m - 1} abla u)$ in a bounded domain $\Omega \subset R^N $ with $u|_{\partial \Omega } = 0$, where $0 0$, i.e., it tends to zero as $t \to T$. Therefore, it is important to know the spatial pattern of $u(x,t)$ as $t \to T^ - $. In this paper we study this problem and prove that the spatial pattern is characterized by solutions which are in the form of separation of variables and have the same extinction time T.