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Well posedness and exponential stability in a wave equation with a strong damping and a strong delay. (English) Zbl 1355.35025

Summary: In this paper, we consider a wave equation with a strong damping and a strong constant (respectively, distributed) delay. We prove the well-posedness and establish an exponential decay result under a suitable assumption on the weight of the damping and the weight of the delay.{
©2016 American Institute of Physics}

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L05 Wave equation
93D15 Stabilization of systems by feedback
93D20 Asymptotic stability in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
49K40 Sensitivity, stability, well-posedness
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