ON LONG TIME BEHAVIOR OF MOORE-GIBSON-THOMPSON EQUATION WITH MOLECULAR RELAXATION

被引：36

作者：

Caixeta, Arthur Henrique ^{[1
]}

Lasiecka, Irena ^{[2
,3
]}

Domingos Cavalcanti, Valeria Neves ^{[4
]}

机构：

[1] Univ Estadual Londrina, Dept Math, Londrina, Parana, Brazil

[2] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[3] Polish Acad Sci, IBS, Memphis, TN USA

[4] Univ Estadual Maringa, Dept Math, Maringa, Parana, Brazil

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2016年 / 5卷 / 04期

关键词：

MGT equation; thermal and molecular relaxation; third order in time equations; viscoelastic-memory dependent dynamics; global solutions for small data; PARTIAL-DIFFERENTIAL-EQUATION; NONLINEAR ACOUSTICS; GENERAL DECAY; EVOLUTION-EQUATIONS; MEMORY; ENERGY; THERMODYNAMICS; PROPAGATION; ATTRACTORS; 3RD-ORDER;

D O I：

10.3934/eect.2016024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A third order in time nonlinear equation is considered. This particular model is motivated by High Frequency Ultra Sound (HFU) technology which accounts for thermal and molecular relaxation. The resulting equations give rise to a quasilinear-like evolution with a potentially degenerate damping [23]. The purpose of this paper is twofold: (1) to provide a brief review of recent results in the area of long time behavior of solutions to of MGT equation, (2) to provide recent results pertaining to decay of energy associated with the model accounting for molecular relaxation which is locally distributed.

引用

页码：661 / 676

页数：16

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