Asymptotic Behavior Of Solutions For The Classical Reaction-diffusion Equation With Nonlinear Boundary Condition And Fading Memory

In this paper,we study the asymptotic behavior of solutions for the classical reaction-diffusion equation with memory and weak memory under the nonlinear boundary con-dition,by using of semigroup theory,abstract function theory and estimation tech-niques,and eventually the existences of global attractors are proved.This paper mainly study two issues:i)Consider the existence of global attractors for the classical reaction-diffusion equa-tion with nonlinear boundary condition and memory:The existence of global attractors was obtained in space L2(Ω)×Lμ2(R+;H1(Ω)),while the external forcing h(x)∈L2(Ω).ii)Consider the existence of global attractors for the classical reaction-diffusion equa-tion with nonlinear boundary condition and weak memory:The existence of global attractors was obtained in space L2(Ω)×Lμ2(R+;L2(Ω)),while the external forcing h(x)∈L2(Q).