Well-posedness and energy decay of a transmission problem of Kirchhoff type wave equations with damping and delay terms
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Date
2021-12-02
Authors
Liu, Zhiqing
Gao, Cunchen
Fang, Zhong Bo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider a transmission problem of Kirchhoff type wave equations with delay and damping terms, subject to a memory condition on one part of the boundary. Under appropriate hypotheses on the relaxation function and the relationship between weights of damping and delay terms, we establish well-posedness of the problem. Using the Faedo-Galerkin approximation technique, and introducing suitable energy and Lyapunov functionals, we obtain estimates for exponential, polynomial, and logarithmic decay.
Description
Keywords
Transmission problem, Kirchhoff type wave equations, Damping, Delay term, Well-posed, Decay estimate
Citation
Liu, Z., Gao, C., & Fang, Z. B. (2021). Well-posedness and energy decay of a transmission problem of Kirchhoff type wave equations with damping and delay terms. <i>Electronic Journal of Differential Equations, 2021</i>(95), pp. 1-23.
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Attribution 4.0 International