On a nonlinear generalized thermoelastic system with obstacle.

*(English)*Zbl 1254.35153The authors study the \(n\)-dimensional semilinear thermoelastic system with unilateral boundary conditions (Signorini’s conditions), which describes the motion of an thermoelastic body in contact with a rigid obstacle without attrition. The authors first reformulate the original contact problem as a variational inequality problem and give an approximate variational problem by introducing a penalty term. Then, by careful energy estimates and the compactness argument, the authors prove the global existence of weak solutions. In the one-dimensional case, the authors are able to exploit the one-dimensional features, such as the better regularity under Signorini’s boundary conditions, to show that the solutions decay exponentially as time goes to infinity.

Reviewer: Song Jiang (Beijing)

##### MSC:

35L86 | Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators |

35B40 | Asymptotic behavior of solutions to PDEs |

35L53 | Initial-boundary value problems for second-order hyperbolic systems |

35L71 | Second-order semilinear hyperbolic equations |

74F05 | Thermal effects in solid mechanics |

74M15 | Contact in solid mechanics |