Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay

Volume 9, Issue 3, pp 1202--1215 http://dx.doi.org/10.22436/jnsa.009.03.46

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Authors

Danhua Wang - College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. Gang Li - College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. Biqing Zhu - College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China.

Abstract

In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypotheses on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove the well-posedness result by using Faedo-Galerkin method. By introducing suitable Lyapunov functionals, we establish a general decay result, from which the exponential and polynomial types of decay are only special cases.

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Keywords

• Wave equation
• transmission problem
• general decay
• viscoelastic term
• delay.

MSC

•  35B37
•  35L55
•  93D15
•  93D20

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