Sufficient Conditions of Blow-up and Bound Estimations of Blow-up Time for a Parabolic Equation in Multi-Dimensional Space

Abstract

In this paper, we establish some sufficient conditions on the heat source function and the heat conduction function of the parabolic equation to guarantee that $u(x,t)$ blows up at finite time, and give upper and lower bounds of the blow-up time in multi-dimensional space.