Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity

Reinhard Racke, Yoshihiro Shibata, Songmu Zheng

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)751-763
Number of pages13
JournalQuarterly of Applied Mathematics
Volume51
Issue number4
Publication statusPublished - 1993 Dec
Externally publishedYes

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Global Smooth Solution
Global Solvability
Thermoelasticity
Exponential Stability
Asymptotic stability
Initial-boundary-value Problem
Dirichlet Problem
Periodic Solution
Corollary
Infinity
Tend
Boundary value problems

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity. / Racke, Reinhard; Shibata, Yoshihiro; Zheng, Songmu.

In: Quarterly of Applied Mathematics, Vol. 51, No. 4, 12.1993, p. 751-763.

Research output: Contribution to journalArticle

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