Exponential stability of a flexible structure with second sound
Volume 122 / 2019
Annales Polonici Mathematici 122 (2019), 71-79 MSC: Primary 35L05; Secondary 37C75, 93D20. DOI: 10.4064/ap171116-31-8 Published online: 9 November 2018
In previous work [Indag. Math. 27 (2016), 821–834], Alves et al. considered a non-uniform flexible structure under Cattaneo’s law of heat conduction, and proved the stabilization to be exponential for zero heat flux on the boundary, and at least polynomial when the temperature satisfies the Dirichlet conditions on the boundary. In this paper, we continue to study the same system and show that the solution is exponentially decaying for the above second set of boundary conditions.