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.
In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation functions, and some properties of convex functions are considered.
In this paper, we prove a general energy decay results of a coupled Lamé system with distributed time delay. By assuming a more general of relaxation functions and using some properties of convex functions, we establish the general energy decay results to the system by using an appropriate Lyapunov functional.
<p style='text-indent:20px;'>In this paper, we consider a wave equation with logarithmic source term and fractional boundary dissipation. We study the global existence of the solution under some conditions and prove the general decay of the solution in this case by using the Lyapunov functional. Also, the blow-up of solution is established at three different levels of energy using the potential well method.</p>
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