Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay
Copyright policy )Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay
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.
- Nanjing University of Information Science and Technology China (People's Republic of)
Asymptotic stability in control theory, transmission problem, delay, Asymptotic behavior of solutions to PDEs, no frictional damping, exponential decay, Lyapunov functionals, viscoelastic, Higher-order hyperbolic systems, QA1-939, wave equation, Stabilization of systems by feedback, Mathematics
Asymptotic stability in control theory, transmission problem, delay, Asymptotic behavior of solutions to PDEs, no frictional damping, exponential decay, Lyapunov functionals, viscoelastic, Higher-order hyperbolic systems, QA1-939, wave equation, Stabilization of systems by feedback, Mathematics
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