Electron. J. Differential Equations, Vol. 2021 (2021), No. 90, pp. 1-14.

Bresse systems with localized Kelvin-Voigt dissipation

Gabriel Aguilera Contreras, Jaime E. Munoz-Rivera

We study the effect of localized viscoelastic dissipation for curved beams. We consider a circular beam with three components, two of them viscous with constitutive laws of Kelvin-Voigt type, one continuous and the other discontinuous. The third component is elastic without any dissipative mechanism. Our main result is that the rate of decay depends on the position of each component. More precisely, we prove that the model is exponentially stable if and only if the viscous component with discontinuous constitutive law is not in the center of the beam. We prove that when there is no exponential stability, the solution decays polynomially.

Submitted March 22, 2021. Published November 4, 2021.
Math Subject Classifications: 35B40, 35P05, 35Q74.
Key Words: Bresse beam; transmission problem; exponential stability; localized viscoelastic dissipative mechanism; polynomial stability.
DOI: https://doi.org/10.58997/ejde.2021.90

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Gabriel Aguilera Contreras
Departamento de Matemática
Universidad del Bío Bío
Concepción, Chile
email: ga.aguilerac@gmail.com, gaaguilera@udec.cl
Jaime E. Muñoz-Rivera
Laboratório Nacional de Computaçao Científica
Petr&ocute;polis, RJ, Brazil
email: jemunozrivera@gmail.com

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