# Global Nonexistence for a Quasilinear Evolution Equation with a Generalized Lewis Function

### Yong Zhou

Shanghai University of Finance and Economics, China

## Abstract

We consider the following quasilinear parabolic equation \begin{eqnarray*} a(x,t) u_t-\mbox{\rm div}\left(|\nabla u|^{m-2} \nabla u \right)=f(u), \end{eqnarray*} where $a(x,t) \geq 0$ is a generalized Lewis function. The main result is that the solution blows up in finite time if the initial datum $u(x,0)$ possesses suitable positive energy. Moreover, we have a precise estimate for the lifespan of the solution in this case. Blowup of solutions with vanishing initial energy is considered also.