The Properties of a Parabolic Equation with Absorb Term and Memory Boundary Condition

In this paper, we studied the following parabolic equation with absorb term u_t=Δu－u^m(x, t), x∈Ω, t>0 under the Neumann boundary condition \frac\partial u\partial v = u^q\int_0^t u^p , where p>0, q>0, m≥1. We proved a comparison principle, and then established the local existence of solutions via a fixed point argument. Finally we obtained the sufficient condition for the existence of blowup solutions by using the super-sub solution technique and integral methods.