Long-time dynamics of the Swift-Hohenberg equations

被引：12

作者：

Khanmamedov, Azer ^{[1
]}

机构：

[1] Hacettepe Univ, Fac Sci, Dept Math, TR-06800 Ankara, Turkey

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 483卷 / 02期

关键词：

Swift-Hohenberg equation; Hyperbolic relaxation; Global attractor; ATTRACTOR; EXISTENCE;

D O I：

10.1016/j.jmaa.2019.123626

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial boundary value problems for the Swift-Hohenberg equation and its hyperbolic relaxation. Under the optimal conditions on the nonlinearity, we prove the well-posedness of the both problems and uniform (with respect to the initial data) global boundedness of the solutions. Then, we show that the both problems possess the global attractors of optimal regularity. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：22

共 22 条

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Cazenave T., 1998, Oxford Lecture Mathematics

[2]

Chueshov I, 2010, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-0-387-87712-9

[3] STRICT MONOTONICITY OF EIGENVALUES AND UNIQUE CONTINUATION [J].