Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay
نویسندگان
چکیده
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.
منابع مشابه
Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping
with initial and Dirichlet boundary conditions. We prove that, under suitable assumptions on the functions gi, fi (i = 1, 2) and certain initial data in the stable set, the decay rate of the solution energy is exponential. Conversely, for certain initial data in the unstable set, there are solutions with positive initial energy that blow up in finite time. 2000 Mathematics Subject Classificatio...
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