Blow-Up Solutions and Global Existence for a Kind of Quasilinear Reaction-Diffusion Equations

摘要

In this paper, we study the blow-up solutions and global existence for a quasilinear reaction-diffusion equation including a gradient term and nonlinear boundary condition: where D ? R~N is a bounded domain with smooth boundary бD. The sufficient conditions are obtained for the existence of a global solution and a blow-up solution. An upper bound for the "blow-up time", an upper estimate of the "blow-up rate", and an upper estimate of the global solution are specified under some appropriate assumptions for the nonlinear system functions f, g, r, a, and initial value u_0 by constructing suitable auxiliary functions and using maximum principles.