Large time behaviour of solutions to a class of quasilinear parabolic equations with convection terms

Abstract

In this paper, we investigate the large time behaviour of solutions to the exterior problems of a class of quasilinear parabolic equations with convection terms. We establish the critical Fujita exponents pc and blow-up theorems of the Fujita type for both homogeneous Neumann and Dirichlet problems. In particular, it is shown that the critical p = pc belongs to the blow-up case under any nontrivial initial data. An interesting phenomenon is exploited that the critical Fujita exponent pc could even be infinite for the considered model because of the nonlinear convection.