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

Abstract

We consider the following quasilinear parabolic equation

where $a(x,t)\ge 0$ 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.