### 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 language | English |
---|---|

Pages (from-to) | 751-763 |

Number of pages | 13 |

Journal | Quarterly of Applied Mathematics |

Volume | 51 |

Issue number | 4 |

Publication status | Published - 1993 Dec |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Quarterly of Applied Mathematics*,

*51*(4), 751-763.

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

Research output: Contribution to journal › Article

*Quarterly of Applied Mathematics*, vol. 51, no. 4, pp. 751-763.

}

TY - JOUR

T1 - Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity

AU - Racke, Reinhard

AU - Shibata, Yoshihiro

AU - Zheng, Songmu

PY - 1993/12

Y1 - 1993/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027835897&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027835897&partnerID=8YFLogxK

M3 - Article

VL - 51

SP - 751

EP - 763

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

SN - 0033-569X

IS - 4

ER -