### 抄録

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.

元の言語 | English |
---|---|

ページ（範囲） | 871-895 |

ページ数 | 25 |

ジャーナル | Mathematical Methods in the Applied Sciences |

巻 | 18 |

発行部数 | 11 |

DOI | |

出版物ステータス | Published - 1995 |

外部発表 | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### これを引用

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

研究成果: Article

}

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 -