Pullback Attractors And Asymptotic Regularity For Nonclassical Diffusion Equations With Delays In Locally Uniform Spaces

In this paper,we consider the long-time behavior of the solutions for the following nonclassical diffusion equation with delays in locally uniform spacesWe first give the definition and the global well-posedness of weak solutions.Then we establish the definition and existence theorem of the pullback attractors in locally uniform spaces.In order to obtain pullback asymptotic compactness and asymptotic regularity for process,we decompose the solution for the above equa-tion with initial conditions and the critical nonlinearity is required to have proper decomposition conditions.Finally we show there is a(C_Hlu¹（R^N）,C_Hp¹（R^N）)-pullback attractor,which is a bounded(inC_Hlu¹（R^N）)subset and pullback attracts bounded subsets ofC_Hlu¹（R^N）with respect to theC_Hp¹（R^N）-norm.