Boundary integral formulations for transient linear thermoelasticity with combined-type boundary conditions


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We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where one of the unknown fields satisfies a Dirichlet boundary condition, while the other one is subject to conditions of Neumann type. In the Laplace domain, combined simple- and double-layer potential boundary integral operators are introduced and proven to be coercive. Based on the Laplace domain estimates, it is possible to prove the existence and uniqueness of solutions in the time domain. This analysis complements previous results that may serve as the mathematical foundation for discretization schemes based on the combined use of the boundary element method and convolution quadrature.

Original languageEnglish (US)
Pages (from-to)3888-3911
Number of pages24
JournalSIAM Journal on Mathematical Analysis
Issue number4
StatePublished - 2021


  • Boundary integral operators
  • Fundamental solution
  • Linear thermoelasticity
  • Time-domain boundary integral equations

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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