科研之友
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摘要
In this article, we study the long-time behaviour of the nonclassical diffusion equation u(t) - Delta u(t) - Du + f(u) = g(x) with critical nonlinearity, where the initial data u(0) is an element of H-0(1)(Omega) and the external forcing term g only belongs to H-1 (Omega). Some asymptotic regularity of solutions in H1+nu (Omega) (for any nu is an element of [0, min{1, N/2 - 1})) has been proved, although its stationary solutions (and so the global attractor) only belong to H-0(1)(Omega).
