摘要：

This article consider, for the following
heat equation

$$\left\{ \begin{array}{ll} \displaystyle\frac{u_t}{|x|^s}-\Delta_p u=u^q ,\ \ &(x,t) \in \Omega \times (0,T),\\ u(x,t)= 0 ,&(x,t) \in \partial \Omega\times(0,T) ,\\ u(x,0)=u_0(x) ,& u_0(x)\ge 0,\quad u_0(x)\not\equiv0 \end{array} \right.$$
the existence of global solution under some conditions and give two sufficient conditions
for the blow up of local solution in finite time, where $\Omega$ is a smooth bounded domain
in $R^N(N >p)$, $0\in \Omega ,\Delta_p u={\rm div}(|\nabla u|^{p-2}\nabla u),0\le s\le 2,
p\ge 2, p-1

Abstract:

This article consider, for the following
heat equation

$$\left\{ \begin{array}{ll} \displaystyle\frac{u_t}{|x|^s}-\Delta_p u=u^q ,\ \ &(x,t) \in \Omega \times (0,T),\\ u(x,t)= 0 ,&(x,t) \in \partial \Omega\times(0,T) ,\\ u(x,0)=u_0(x) ,& u_0(x)\ge 0,\quad u_0(x)\not\equiv0 \end{array} \right.$$
the existence of global solution under some conditions and give two sufficient conditions
for the blow up of local solution in finite time, where $\Omega$ is a smooth bounded domain
in $R^N(N >p)$, $0\in \Omega ,\Delta_p u={\rm div}(|\nabla u|^{p-2}\nabla u),0\le s\le 2,
p\ge 2, p-1

中图分类号: 

• 35K20