Version 1
: Received: 18 January 2017 / Approved: 19 January 2017 / Online: 19 January 2017 (10:53:04 CET)
How to cite:
Li, G.; Kong, X. Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays. Preprints2017, 2017010087. https://doi.org/10.20944/preprints201701.0087.v1
Li, G.; Kong, X. Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays. Preprints 2017, 2017010087. https://doi.org/10.20944/preprints201701.0087.v1
Li, G.; Kong, X. Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays. Preprints2017, 2017010087. https://doi.org/10.20944/preprints201701.0087.v1
APA Style
Li, G., & Kong, X. (2017). Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays. Preprints. https://doi.org/10.20944/preprints201701.0087.v1
Chicago/Turabian Style
Li, G. and Xiangyu Kong. 2017 "Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays" Preprints. https://doi.org/10.20944/preprints201701.0087.v1
Abstract
In this paper, we study a one-dimensional Bresse-Cattaneo system with infinite memories and time-dependent delay term (the coefficient of which is not necessarily positive) in the internal feedbacks. First, it is proved that the system is well-posed by means of the Hille-Yosida theorem under suitable assumptions on the relaxation functions. Then, without any restriction on the speeds of wave propagations, we establish the exponential or general decay result by introducing suitable energy and Lyapunov functionals.
Computer Science and Mathematics, Applied Mathematics
Copyright:
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