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Global attractors for a class of semilinear degenerate parabolic equations
Open Mathematics ( IF 1.7 ) Pub Date : 2021-01-01 , DOI: 10.1515/math-2021-0018
Kaixuan Zhu 1 , Yongqin Xie 2
Affiliation  

In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity f f satisfying the polynomial growth of arbitrary p − 1 p-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 ( L 2 ( Ω ) , L p ( Ω ) ) \left({L}^{2}\left(\Omega ),{L}^{p}\left(\Omega )) -global attractors immediately; moreover, such an attractor can attract every bounded subset of L 2 ( Ω ) {L}^{2}\left(\Omega ) with the L p + δ {L}^{p+\delta } -norm for any δ ∈ [ 0 , + ∞ ) \delta \in \left[0,+\infty ) .

中文翻译:

一类半线性退化抛物方程的整体吸引子

在本文中,我们考虑了一类具有非线性ff满足任意p − 1 p-1阶多项式增长的半线性退化抛物方程的长时间行为。我们建立了一些新的估计,即渐近高阶可积性在初始时间附近的解的差异。作为应用程序,我们获得(L 2(Ω),L p(Ω))\ left({L} ^ {2} \ left(\ Omega),{L} ^ {p} \ left(\ Omega) )-立即吸引全球;此外,对于任何δ∈,这样的吸引子都可以吸引L 2(Ω){L} ^ {2} \ left(\ Omega)的每个有界子集,其中L p +δ{L} ^ {p + \ delta} -norm [0,+∞)\ delta \ in \ left [0,+ \ infty)。
更新日期:2021-01-01
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