Global well-posedness and optimal decay rates for a transmission problem of viscoelastic wave equations with degenerate nonlocal damping

This paper investigates a transmission problem of viscoelastic wave equations with degenerate nonlocal damping. We prove the global well-posedness of the problem with the aid of Faedo-Galerkin technique and the multiplier method. Meantime, by introducing a new Lyapunov functional, we establish the optimal explicit and general energy decay results.

Automated summary

This paper investigates a transmission problem of viscoelastic wave equations with degenerate nonlocal damping. The global well-posedness of the problem is proved using Faedo-Galerkin technique and the multiplier method. Meanwhile, by introducing a new Lyapunov functional, the optimal explicit and general energy decay results are established.