Abstract
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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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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DOI: https://doi.org/10.1007/s00028-015-0286-2