In this article, we consider a transmission problem in a bounded domain with a distributed delay in the first equation. Using a semigroup theorem, we prove the existence and uniqueness of global solution under suitable assumptions on the weight of damping and the weight of distributed delay. Also we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
Submitted April 10, 2017. Published July 10, 2017.
Math Subject Classifications: 35B37, 35L55, 74D05, 93D15, 93D20.
Key Words: Transmission problem; distributed delay; exponential decay.
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| Gongwei Liu |
College of Science
Henan University of Technology
Zhengzhou 450001, China
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