## Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic ModelsThis book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike. |

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### Contents

1 | |

2 Exponential Stability for Nonlinear Thermoelastic Equations with Second Sound | 27 |

3 Energy Decay for a TimoshenkoType System with a Past History | 50 |

4 Stability for a Timoshenkotype Thermoelastic Equations of Type III with a Past History | 73 |

5 Global Existence of Solutions for the Thermoelastic Bresse System | 97 |

6 Stability for a Thermoelastic Bresse System | 110 |

7 Global Existence and Exponential Stabilization for the HigherDimensional Linear Thermoelastic System of Type III | 121 |

8 Global Existence for the ThreeDimensional Thermoelastic Equations of Type II | 153 |

9 Energy Decay for Thermoviscoelastic Systems | 165 |

References | 187 |

Index | 199 |

### Other editions - View all

Global Well-posedness and Asymptotic Behavior of the Solutions to Non ... Yuming Qin,Zhiyong Ma No preview available - 2016 |

### Common terms and phrases

Anal Appl asymptotic behavior asymptotic stability Banach space beam boundary conditions chapter Co-semigroup damping decays exponentially deduce defined denotes dissipative domain exists a constant exponential decay exponential stability follows global existence Global Well-posedness H-co heat conduction heat equation Hilbert space initial data inner product Lemma linear thermoelastic Lyapunov functional Math Messaoudi Multiplying Muñoz Rivera nonlinear nonlinear thermoelastic obtain one-dimensional Pazy polynomial positive constants proof of Theorem prove relaxation function s)ds satisfies second sound semigroup ſº dsdy ſº dT solution of problem Solutions to Non-classical space dimension Springer Science+Business Media system of type temperature theory thermal thermoelastic plate thermoelastic system thermoelasticity of type thermoviscoelastic Timoshenko system velocity feedback viscoelastic wave speeds Well-posedness and Asymptotic Wººdy Young's inequality Zheng Zuazua