Global attractors for a class of semilinear degenerate parabolic equations

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 solu...

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Autores principales:	Zhu Kaixuan, Xie Yongqin
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	degenerate parabolic equations polynomial growth of arbitrary order asymptotic higher-order integrability global attractors 35b40 35b41 35k65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/42aa706084df4166a2f9ba49938f5232
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id	oai:doaj.org-article:42aa706084df4166a2f9ba49938f5232
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spelling	oai:doaj.org-article:42aa706084df4166a2f9ba49938f52322021-12-05T14:10:52ZGlobal attractors for a class of semilinear degenerate parabolic equations2391-545510.1515/math-2021-0018https://doaj.org/article/42aa706084df4166a2f9ba49938f52322021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0018https://doaj.org/toc/2391-5455In 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 ).Zhu KaixuanXie YongqinDe Gruyterarticledegenerate parabolic equationspolynomial growth of arbitrary orderasymptotic higher-order integrabilityglobal attractors35b4035b4135k65MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 212-224 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	degenerate parabolic equations polynomial growth of arbitrary order asymptotic higher-order integrability global attractors 35b40 35b41 35k65 Mathematics QA1-939
spellingShingle	degenerate parabolic equations polynomial growth of arbitrary order asymptotic higher-order integrability global attractors 35b40 35b41 35k65 Mathematics QA1-939 Zhu Kaixuan Xie Yongqin Global attractors for a class of semilinear degenerate parabolic equations
description	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 ).
format	article
author	Zhu Kaixuan Xie Yongqin
author_facet	Zhu Kaixuan Xie Yongqin
author_sort	Zhu Kaixuan
title	Global attractors for a class of semilinear degenerate parabolic equations
title_short	Global attractors for a class of semilinear degenerate parabolic equations
title_full	Global attractors for a class of semilinear degenerate parabolic equations
title_fullStr	Global attractors for a class of semilinear degenerate parabolic equations
title_full_unstemmed	Global attractors for a class of semilinear degenerate parabolic equations
title_sort	global attractors for a class of semilinear degenerate parabolic equations
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/42aa706084df4166a2f9ba49938f5232
work_keys_str_mv	AT zhukaixuan globalattractorsforaclassofsemilineardegenerateparabolicequations AT xieyongqin globalattractorsforaclassofsemilineardegenerateparabolicequations
_version_	1718371642790379520

Global attractors for a class of semilinear degenerate parabolic equations

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