Existence and upper semi-continuity of pullback attractors of a p-Laplacian equation with delay

Linfang Liu; Xianlong Fu

doi:10.1063/1.5000076

Existence and upper semi-continuity of pullback attractors of a p-Laplacian equation with delay

Linfang Liu
, Xianlong Fu^*

^*此作品的通讯作者

数学科学学院

East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

8 引用（Scopus）

摘要

In this paper, we study the dynamics of a non-autonomous p-Laplacian equation with delay. We first prove the existence and uniqueness of solutions for this equation by using the Galerkin approximations. Then, applying the Sobolev compactness theorem, Ascoli-Azerla theorem, and energy method, we show the existence of pullback attractors for the associated process in space C([h, 0]; L^p) as well as in space C([h, 0]; L²). The upper semi-continuity result of the pullback attractors is also established here.

源语言	英语
文章编号	082702
期刊	Journal of Mathematical Physics
卷	58
期	8
DOI	https://doi.org/10.1063/1.5000076
出版状态	已出版 - 1 8月 2017

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N2 - In this paper, we study the dynamics of a non-autonomous p-Laplacian equation with delay. We first prove the existence and uniqueness of solutions for this equation by using the Galerkin approximations. Then, applying the Sobolev compactness theorem, Ascoli-Azerla theorem, and energy method, we show the existence of pullback attractors for the associated process in space C([h, 0]; Lp) as well as in space C([h, 0]; L2). The upper semi-continuity result of the pullback attractors is also established here.

AB - In this paper, we study the dynamics of a non-autonomous p-Laplacian equation with delay. We first prove the existence and uniqueness of solutions for this equation by using the Galerkin approximations. Then, applying the Sobolev compactness theorem, Ascoli-Azerla theorem, and energy method, we show the existence of pullback attractors for the associated process in space C([h, 0]; Lp) as well as in space C([h, 0]; L2). The upper semi-continuity result of the pullback attractors is also established here.

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Existence and upper semi-continuity of pullback attractors of a p-Laplacian equation with delay

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