Electron. J. Diff. Equ., Vol. 2016 (2016), No. 23, pp. 1-21.

Well-posedness and decay of solutions for a transmission problem with history and delay

Gang Li, Danhua Wang, Biqing Zhu

Abstract:
In this article, we consider a transmission problem in the presence of history and delay terms. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove well-posedness by using the semigroup theory. Also we establish a decay result by introducing a suitable Lyaponov functional.

Submitted March 20, 2015. Published January 13, 2016.
Math Subject Classifications: 35B37, 35L55, 74D05, 93D15, 93D20.
Key Words: Wave equation; transmission problem; past history; delay term.

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Gang Li
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
Nanjing 210044, China
email: ligang@nuist.edu.cn
Danhua Wang
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
Nanjing 210044, China
email: matdhwang@yeah.net
Biqing Zhu
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
Nanjing 210044, China
email: brucechu@163.com

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