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Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks

The authors are supported by CNEPRU-ALGERIA.
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  • In this paper, we investigate the nonlinear wave equation in a bounded domain with a time-varying delay term in the weakly nonlinear internal feedback

    $\left(|u_{t}|^{\gamma-2}u_{t}\right)_{t}-Lu-\int_{0}^{t}g(t-s)L u(s)ds+ \mu_{1} \psi(u_{t}(x, t))+ \mu_{2} \psi(u_{t}(x, t-\tau(t)))=0.$

    The asymptotic behavior of solutions is studied by using an appropriate Lyapunov functional. Moreover, we extend and improve the previous results in the literature.

    Mathematics Subject Classification: Primary:35L05, 35L15;Secondary:93D15.


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