Global attractors for a class of semilinear degenerate parabolic equations

• Main Authors: Zhu Kaixuan, Xie Yongqin
• Format: Article
• Language: English
• Published: De Gruyter 2021-05-01
• Series: Open Mathematics
• Subjects: degenerate parabolic equations; polynomial growth of arbitrary order; asymptotic higher-order integrability; global attractors; 35b40; 35b41; 35k65
• Online Access: https://doi.org/10.1515/math-2021-0018

In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity ff satisfying the polynomial growth of arbitrary p−1p-1 order. We establish some new estimates, i.e., asymptotic higher-order integrability for the difference of the solutions near the initial time. As an application, we obtain the (L2(Ω),Lp(Ω))\left({L}^{2}\left(\Omega ),{L}^{p}\left(\Omega ))-global attractors immediately; moreover, such an attractor can attract every bounded subset of L2(Ω){L}^{2}\left(\Omega ) with the Lp+δ{L}^{p+\delta }-norm for any δ∈[0,+∞)\delta \in \left[0,+\infty ).