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

In this paper,we study the asymptotic behavior of solutions for the nonautonomous classical reaction-diffusion equation with fading memory or weak fading memory under the nonlinear boundary condition,by use of process theory,contractive function theory and the new priori estimating techniques,eventually the existence and topological structure of uniform attractors are obtained.This paper mainly study the two class of equations:i)the non-autonomous classical reaction-diffusion equation with nonlinear boundary condition and fading memory:where ? is a bounded domain with a smooth boundary ? of R3.The existence and the topological structure of uniform attractors are obtained in the space L²(?)×L_?²(R⁺;H¹₀(?)),while the external forcing h?L_b²(R;L²(?)).ii)the non-autonomous classical reaction-diffusion equation with nonlinear boundary condition and weak fading memory:where ? is a bounded domain with a smooth boundary ? of R3.The existence and the topological structure of uniform attractors are achieved in the space L²(?)×L_?²(R⁺;L²(?)),while the external forcing h?L_b²(R;L²(?)).