INERTIAL MANIFOLDS FOR THE HYPERBOLIC RELAXATION OF SEMILINEAR PARABOLIC EQUATIONS

被引：8

作者：

Chepyzhov, Vladimir V. ^{[1
,2
]}

Kostianko, Anna ^{[3
]}

Zelik, Sergey ^{[3
]}

机构：

[1] Russian Acad Sci, Inst Informat Transmiss Problems, Bolshoy Karetniy 19, Moscow 127051, Russia

[2] Voronezh State Univ, Univ Skaya Sq 1, Voronezh 394018, Russia

[3] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 03期

基金：

英国工程与自然科学研究理事会; 俄罗斯基础研究基金会;

关键词：

Hyperbolic relaxation; gap property; inertial manifold; INTEGRAL MANIFOLDS; WAVE-EQUATIONS; ATTRACTORS; COUNTEREXAMPLES; REGULARITY; EXISTENCE; FORMS;

D O I：

10.3934/dcdsb.2019009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested and optimal spectral gap conditions which guarantee their existence are established. Moreover, the dependence of the constructed manifolds on the relaxation parameter in the case of the parabolic singular limit is also studied.

引用

页码：1115 / 1142

页数：28

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