On the stability of Timoshenko systems with Gurtin-Pipkin thermal law
Filippo Dell'Oro, Vittorino Pata
TL;DR
This paper investigates the exponential stability of Timoshenko beam models coupled with Gurtin-Pipkin thermal law, providing a comprehensive condition based on system parameters and generalizing earlier models.
Contribution
It establishes a necessary and sufficient stability condition for Timoshenko systems with Gurtin-Pipkin thermal law, extending previous Fourier and Cattaneo models.
Findings
Exponential stability condition derived
Generalization of Fourier-Timoshenko and Cattaneo-Timoshenko models
Structural parameters determine stability
Abstract
We analyze a differential system describing a Timoshenko beam coupled with a temperature evolution of Gurtin-Pipkin type. A necessary and sufficient condition for exponential stability is established in terms of the structural parameters of the equations. In particular, we generalize previously known results on the Fourier-Timoshenko and the Cattaneo-Timoshenko beam models.
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