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

Danhua Wang, Gang Li and Biqing Zhu
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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

Mathematics, 2016, vol. 4, issue 2, 1-13

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.

Keywords: wave equation; transmission problem; exponential decay; viscoelastic; delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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