Generalised energy conservation law for wave equations with variable propagation speed

被引：19

作者：

Hirosawa, Fumihiko ^{[1
]}

Wirth, Jens ^{[2
]}

机构：

[1] Yamaguchi Univ, Dept Math, Yamaguchi 7538512, Japan

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 358卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

A priori estimates; Wave equations; Generalised energy conservation law; Floquet theory; HYPERBOLIC-EQUATIONS; COEFFICIENTS; TIME;

D O I：

10.1016/j.jmaa.2009.04.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the long time behaviour of the L-2-energy of solutions to wave equations with variable speed of propagation. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation property. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：56 / 74

页数：19

共 17 条

[1] HYPERBOLIC-EQUATIONS WITH COEFFICIENTS RAPIDLY OSCILLATING IN TIME - A RESULT OF NONSTABILITY [J].

COLOMBINI, F ;

SPAGNOLO, S .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1984, 52 (01) :24-38

[2] Energy estimates at infinity for hyperbolic equations with oscillating coefficients [J].

Colombini, Ferruccio .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 231 (02) :598-610

[3]

Galstian A., 2003, APPL ANAL, V82, P197, DOI DOI 10.1080/0003681031000063720

[4] Cm-theory of damped wave equations with stabilisation [J].

Hirosawa, Fumihiko ;

Wirth, Jens .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (02) :1022-1035

[5] On the asymptotic behavior of the energy for the wave equations with time depending coefficients [J].

Hirosawa, Fumihiko .

MATHEMATISCHE ANNALEN, 2007, 339 (04) :819-838

[6]

MAGNUS W, 1966, HILLS EQUATION, V8

[7]

Reissig M, 1999, MATH METHOD APPL SCI, V22, P937, DOI 10.1002/(SICI)1099-1476(19990725)22:11<937::AID-MMA28>3.0.CO

[8]

2-O

[9]

Reissig M, 2000, MATH NACHR, V214, P71, DOI 10.1002/1522-2616(200006)214:1<71::AID-MANA71>3.3.CO

[10]

2-3

← 1 2 →