Global existence and blowup of solutions of the heat equation with a memory boundary of polynomial type

Abstract

This paper deals with the long time behavior of solutions of the heat equation with a memory boundary of polynomial type. We rst establish the comparison principle and prove the local existence of classical solutions. Then we study the global existence and blowup of the solutions by using the comparison principle and Greens function. At last, we consider the boundary blowup and the blowup rate.