Solvability and Blow-up of Solutions of Semi Linear Parabolic Problem with Integral Condition of Second Type

Abstract

In this paper, semi-linear parabolic equation with integral boundary condition of second type is investigated. The existence, uniqueness and Blow-up of weak solutions in finite time are established. The proof is proceeds in two steps; using the variable separation method for the solvability of the linear cas and applying an iterative process and a priori estimate, we prove the existence, uniqueness of the weak solution of the semilinear problem. Finally, we study a blow-up of solution in finite time for a super-linear problem by using eigen functions method introduced by Kaplan.