Blow-up Problem For A Class Of Non-Classical Heat Equation With Memory Term

In this article,we consider a non-classical heat equation with a memory boundary condition.We have proved that our solutions blow-up in the finite time,and blow-up only occur on the boundary.Firstly,we construct the classical solution by using the Green function and Banach fixed point theorem.And then we prove the solution blowup in the finite time.Last,we prove the solution only occur on the boundary by using the theorem 4.1.1.