Preprint Article Version 1 This version is not peer-reviewed

Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays

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. Preprints 2017, 2017010087 (doi: 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 (doi: 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.

Subject Areas

well-posedness; asymptotic stability; infinite memory; Cattaneo's law; time-varying delay

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