Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity

Authors:
Reinhard Racke, Yoshihiro Shibata and Song Mu Zheng

Journal:
Quart. Appl. Math. **51** (1993), 751-763

MSC:
Primary 35Q72; Secondary 35B35, 73B30, 73C50

DOI:
https://doi.org/10.1090/qam/1247439

MathSciNet review:
MR1247439

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Abstract | References | Similar Articles | Additional Information

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 righthand sides.

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DOI:
https://doi.org/10.1090/qam/1247439

Article copyright:
© Copyright 1993
American Mathematical Society