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

Abstract

In this article, we study the long-time behaviour of the nonclassical diffusion equation u t − Δu t − Δu + f(u) = g(x) with critical nonlinearity, where the initial data and the external forcing term g only belongs to H −1(Ω). Some asymptotic regularity of solutions in H 1+ν(Ω) (for any ) has been proved, although its stationary solutions (and so the global attractor) only belong to .