Version 1
: Received: 12 February 2017 / Approved: 13 February 2017 / Online: 13 February 2017 (09:37:37 CET)
Version 2
: Received: 19 February 2017 / Approved: 20 February 2017 / Online: 20 February 2017 (06:36:23 CET)
How to cite:
Liu, W.; Chen, D.; Zhu, B. Global Existence and Exponential Decay for a Dynamic Contact Problem of Thermoelastic Timoshenko Beam with Second Sound. Preprints2017, 2017020038. https://doi.org/10.20944/preprints201702.0038.v2
Liu, W.; Chen, D.; Zhu, B. Global Existence and Exponential Decay for a Dynamic Contact Problem of Thermoelastic Timoshenko Beam with Second Sound. Preprints 2017, 2017020038. https://doi.org/10.20944/preprints201702.0038.v2
Liu, W.; Chen, D.; Zhu, B. Global Existence and Exponential Decay for a Dynamic Contact Problem of Thermoelastic Timoshenko Beam with Second Sound. Preprints2017, 2017020038. https://doi.org/10.20944/preprints201702.0038.v2
APA Style
Liu, W., Chen, D., & Zhu, B. (2017). Global Existence and Exponential Decay for a Dynamic Contact Problem of Thermoelastic Timoshenko Beam with Second Sound. Preprints. https://doi.org/10.20944/preprints201702.0038.v2
Chicago/Turabian Style
Liu, W., Dongqin Chen and Biqing Zhu. 2017 "Global Existence and Exponential Decay for a Dynamic Contact Problem of Thermoelastic Timoshenko Beam with Second Sound" Preprints. https://doi.org/10.20944/preprints201702.0038.v2
Abstract
In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo's law instead of the usual Fourier's law. The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effects of heat conduction induced by Cattaneo's law. By considering related penalized problems, proving some a priori estimates and passing to the limit, we prove the global existence of the solutions. By considering the approximate framework, constructing some new functionals and applying the perturbed energy method, we obtain the exponential decay result for the approximate solution, and then prove the exponential decay rate to the original problem by utilizing the weak lower semicontinuity arguments.
Keywords
thermoelastic Timoshenko beam; global existence; exponential stability; second sound
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.