Blow-up, global existence and exponential decay estimates for a class of quasilinear parabolic problems

This paper deals with a class of nonlinear parabolic problems in divergence form whose solutions, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to establish conditions on the data sufficient to guarantee blow-up of solution at some finite time ττ, conditions to ensure that the solution remains bounded as well as conditions to derive some explicit exponential decay bounds for the solution and its derivatives.