A nonlinear thermoelastic system with nonlinear boundary conditions


In this paper, we give a mathematical treatment of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to nonlinear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonlinear nonlocal thermoelastic coupled system under nonlinear boundary conditions.

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Correspondence to H. R. Clark.

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Clark, H.R., Clark, M.R., Louredo, A.T. et al. A nonlinear thermoelastic system with nonlinear boundary conditions. J. Evol. Equ. 15, 895–911 (2015). https://doi.org/10.1007/s00028-015-0286-2

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Mathematics Subject Classification

  • 35L15
  • 35L20
  • 35K55
  • 35L60
  • 35L70


  • Thermoelastic coupled system
  • Nonlinear boundary condition
  • Existence
  • Uniqueness and stabilization uniform of the solutions