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Stability for coupled thermoelastic systems with nonlinear localized dam** and Wentzell boundary conditions

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Abstract

This paper is concerning with the study of stability involving a thermoelastic system with internal nonlinear localized dam**. The main novelty of the paper is to introduce to the study of thermoelastic system the general Wentzell boundary conditions associated to the internal heat equation. This boundary condition takes into account that there is a boundary source of heat which depends on the heat flow along the boundary, the heat flux across the boundary, and the temperature at the boundary. The tools are the use of multipliers with the construction of appropriate perturbed energy functionals.

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Authors and Affiliations

  1. CCET, Western Paraná State University, Rua Universitária, 2069, Cascavel, Paraná, 85819-110, Brazil

    André Vicente

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  1. André Vicente
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Correspondence to André Vicente.

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Communicated by Jerome A. Goldstein.

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Research of André Vicente is partially supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq, Grant 306771/2023-3.

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Vicente, A. Stability for coupled thermoelastic systems with nonlinear localized dam** and Wentzell boundary conditions. Semigroup Forum 108, 734–758 (2024). https://doi.org/10.1007/s00233-024-10445-7

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