Asymptotic dynamics of semilinear thermoelastic Timoshenko systems

Marcio A. Jorge Silva; Rodrigo N. Monteiro; Thales M. Souza

doi:10.3934/dcdss.2025031

Article Contents

2025, Volume 18, Issue 7: 2027-2046. Doi: 10.3934/dcdss.2025031

This issue Previous Article On a fourth-order Allen-Cahn type equation with degenerate mobility Next Article Global relaxation limit for relaxed full compressible Navier-Stokes equations

Asymptotic dynamics of semilinear thermoelastic Timoshenko systems

1.
Department of Mathematics, State University of Londrina, Londrina 86057-970, Paraná, Brazil
2.
Department of Mobility Engineering, Federal University of Santa Catarina, 89219-600 Joinville, SC, Brazil

^*Corresponding author: Marcio A. Jorge Silva
^*Corresponding author: Marcio A. Jorge Silva

Received: July 2024

Revised: February 2025

Early access: March 2025

Published: July 2025

The first author is supported by the CNPq Grant 309929/2022-9 and Fundação Araucária Grant 226/2022.

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Abstract

This paper investigates a class of semilinear Timoshenko systems with thermal coupling on both the bending moment and the shear force. Under some general assumptions, we conclude the global well-posedness of the system. Then, we establish the existence of a compact global attractor with finite fractal dimension. In particular, under some proper assumptions, our results also allow to reach the uniform exponential stability of solutions.

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Mathematics Subject Classification: Primary: 35B41, 35Q74, 37L30; Secondary: 74F05, 74H40.

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References

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