### Abstract

We prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non‐linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.

Original language | English |
---|---|

Pages (from-to) | 871-895 |

Number of pages | 25 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 18 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

**Global in time existence of small solutions of non‐linear thermoviscoelastic equations.** / Shibata, Yoshihiro.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Global in time existence of small solutions of non‐linear thermoviscoelastic equations

AU - Shibata, Yoshihiro

PY - 1995

Y1 - 1995

N2 - We prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non‐linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.

AB - We prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non‐linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.

UR - http://www.scopus.com/inward/record.url?scp=84988201424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988201424&partnerID=8YFLogxK

U2 - 10.1002/mma.1670181104

DO - 10.1002/mma.1670181104

M3 - Article

VL - 18

SP - 871

EP - 895

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 11

ER -