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Mathematics 2016, 4(2), 42; doi:10.3390/math4020042

Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay

College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
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Academic Editors: Reza Abedi and Indranil SenGupta
Received: 7 January 2016 / Revised: 3 June 2016 / Accepted: 6 June 2016 / Published: 9 June 2016
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
View Full-Text   |   Download PDF [270 KB, uploaded 9 June 2016]

Abstract

In our previous work (Journal of Nonlinear Science and Applications 9: 1202–1215, 2016), we studied the well-posedness and general decay rate for a transmission problem in a bounded domain with a viscoelastic term and a delay term. In this paper, we continue to study the similar problem but without the frictional damping term. The main difficulty arises since we have no frictional damping term to control the delay term in the estimate of the energy decay. By introducing suitable energy and Lyapunov functionals, we establish an exponential decay result for the energy. View Full-Text
Keywords: wave equation; transmission problem; exponential decay; viscoelastic; delay wave equation; transmission problem; exponential decay; viscoelastic; delay
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Wang, D.; Li, G.; Zhu, B. Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay. Mathematics 2016, 4, 42.

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