Global solutions of the Neumann problem in one-dimensional nonlinear thermoelasticity.

*(English)*Zbl 0786.73009The paper deals with the existence and uniqueness of global solutions of the initial-boundary value problem (Neumann problem with stress-free, insulated boundaries) of one-dimensional coupled thermoelasticity. The constitutive relations are somewhat simplified by assuming that heat flux depends only on the temperature gradient. The Neumann problem is considered with stress free, insulated boundaries. The initial conditions on displacement gradient, velocity and temperature are supposed to be given. Based on some assumptions concerning constitutive relations and initial data, a global existence and uniqueness theorem is proved by carefully and deftly evaluating certain norm estimates in appropriate Sobolev spaces. Decay rate of solutions to the linearized problem is also calculated.

Reviewer: E.S.Suhubi (İstanbul)

##### MSC:

74A15 | Thermodynamics in solid mechanics |

74B99 | Elastic materials |

35Q72 | Other PDE from mechanics (MSC2000) |

35D05 | Existence of generalized solutions of PDE (MSC2000) |

35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |

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\textit{S. Jiang}, Nonlinear Anal., Theory Methods Appl. 19, No. 2, 107--121 (1992; Zbl 0786.73009)

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