Asymptotic regularity for the nonclassical diffusion equation with lower regular forcing term

摘要

In this article, we study the long-time behaviour of the nonclassical diffusion equation u_t- △u_t,-△_u+f(u)= g(x) with critical nonlinearity, where the initial data u_0 ∈H_0~1(Ω) and the external forcing term g only belongs to H~-1(Ω). Some asymptotic regularity of solutions in H~(1+v)(Ω) (for any v ∈[0, min{l, N/2-1})) has been proved, although its stationary solutions (and so the global attractor) only belong to H~1_0(Ω).