Uniform Energy Decay Rate And Blow-up Of Solution For The Semilinear Parabolic Equation With A Memory Term

In this thesis, we are concerned with an mixed boundary value problem forsemilinear parabolic equation with a memory term by introducing brief Lyapunovfunction, precise priori estimates and the method of perturbation energy.First, we introduce the development of the problem, define the space,scalarproducts and norms.Next, we investigate global existence for semilinear parabolic equation with amemory term and mixed boundary condition, and establish the energy functionaldecays exponentially or polynomially to zero as the time goes to infinity, wheng(t) decays exponentially or polynomially to zero.Then, we investigate two kinds of the semilinear parabolic equation with amemory term and mixed boundary condition, and establish the energy functionaldecays in diferent ways when when g(t) has diferent conditions.The last, we investigate the blow-up of positive initial energy solutions forthe semilinear parabolic equation with a memory term and mixed boundarycondition.