Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity

Racke, Reinhard; Shibata, Yoshihiro; Zheng, Song Mu

doi:10.1090/qam/1247439

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: 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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