Zhiqing Liu, Cunchen Gao, Zhong Bo Fang
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.
Submitted April 5, 2021. Published December 2, 2021.
Math Subject Classifications: 35B40, 35L51.
Key Words: Transmission problem; Kirchhoff type wave equations; damping;
delay term; well-posed; decay estimate.
DOI: https://doi.org/10.58997/ejde.2021.95
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Zhiqing Liu School of Mathematics and Physics Qingdao University of Science and Technology Qingdao 266061, China email: Lzhiqing1005@163.com |
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Cunchen Gao School of Mathematical Sciences Ocean University of China Qingdao 266100, China email: ccgao123@126.com |
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Zhong Bo Fang School of Mathematical Sciences Ocean University of China Qingdao 266100, China email: fangzb7777@hotmail.com |
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