Abstract:

In this paper, we consider the long-time behavior of solutions for a class of reaction-diffusion equations in $\Bbb R ^{n}$ with weighted terms $V(x)$ and some distribution derivatives in inhomogeneous terms. We prove that the $\big(L^{2}(\Bbb R ^{n}), L^{2}(\Bbb R ^{n})\cap L^{p}(\Bbb R ^{n})\big)$-global attractors indeed can attract every bounded subset of $L^{2}(\Bbb R ^{n})$ with the $L^{2}\cap L^{p+\delta_{1}}$-norm for any $\delta_{1}\in [0,+\infty)$.

Key words: Reaction-diffusion equations, Asymptotic higher-order integrability, Global attractors