GLOBAL SOLVABILITY AND EXPONENTIAL STABILITY IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY

被引：42

作者：

RACKE, R

SHIBATA, Y

ZHENG, SM

机构：

[1] UNIV TSUKUBA,INST MATH,TSUKUBA,IBARAKI 305,JAPAN

[2] FUDAN UNIV,INST MATH,SHANGHAI,PEOPLES R CHINA

来源：

QUARTERLY OF APPLIED MATHEMATICS | 1993年 / 51卷 / 04期

关键词：

NONLINEAR THERMOELASTICITY; GLOBAL EXISTENCE AND UNIQUENESS; ASYMPTOTIC BEHAVIOR; PERIODIC SOLUTION;

D O I：

10.1090/qam/1247439

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are mainly concerned with the Dirichlet initial boundary value problem in one-dimensional nonlinear thermoelasticity. It is proved that if the initial data are close to the equilibrium then the problem admits a unique, global, smooth solution. Moreover, as time tends to infinity, the solution is exponentially stable. As a corollary we also obtain the existence of periodic solutions for small, periodic right-hand sides.

引用

页码：751 / 763

页数：13

共 17 条

[1] DEVELOPMENT OF SINGULARITIES IN SOLUTIONS OF THE EQUATIONS OF NONLINEAR THERMOELASTICITY [J].

DAFERMOS, CM ;

HSIAO, L .

QUARTERLY OF APPLIED MATHEMATICS, 1986, 44 (03) :463-474

[2] ON SMOOTH SOLUTIONS OF THE CAUCHY-PROBLEM IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY [J].

HRUSA, WJ ;

TARABEK, MA .

QUARTERLY OF APPLIED MATHEMATICS, 1989, 47 (04) :631-644

[3] ON FORMATION OF SINGULARITIES IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY [J].

HRUSA, WJ ;

MESSAOUDI, SA .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1990, 111 (02) :135-151

[4] GLOBAL-SOLUTIONS OF THE NEUMANN PROBLEM IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY [J].

JIANG, S .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (02) :107-121

[5] GLOBAL EXISTENCE OF SMOOTH SOLUTIONS IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY [J].

JIANG, S .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1990, 115 :257-274

[6]

JIANG S, 1990, SFB256 U BONN

[7]

Kawashima S., 1983, THESIS KYOTO U, DOI DOI 10.14989/DOCTOR.K3193

[8]

KAWASHIMA S, 1982, P JAP ACAD A, V53, P384

[9] GLOBAL, SMALL AMPLITUDE SOLUTIONS TO NON-LINEAR EVOLUTION-EQUATIONS [J].

KLAINERMAN, S ;

PONCE, G .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (01) :133-141

[10]

MATSUMURA A, 1977, PUBL RIMS KYOTO U, V13, P349

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