## 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.{

### 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

### Keywords:

well-posedness; exponential decay
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### References:

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