Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

Abstract

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation: $\partial u/\partial t=ℒu+V\left(w\right)u^{p-1}$ in $\Omega \times \left(0,T\right)$, , $u\left(w,0\right)=u_0\left(w\right)\ge 0$ in $\Omega$, $u\left(w,t\right)=0$ on $\partial \Omega \times \left(0,T\right)$ where $ℒ$ is the subelliptic $p$-Laplacian and $V\in L_{loc}^1\left(\Omega \right)$.