Existence and General Decay of Coupled Viscoelastic Waves System
DOI:
https://doi.org/10.64229/ht0b7z95Keywords:
Wave system, General decay, Viscoelastic term, Global existenceAbstract
In this work, we study a coupled wave system with viscoelastic damping subject to Dirichlet boundary conditions on For a broad class of relaxation functions, we employ the Faedo–Galerkin method, combined with suitable a priori estimates, to establish the global existence and uniqueness of solutions. To investigate the asymptotic behavior, we use Lyapunov’s method together with convexity arguments to derive general decay results. By constructing an appropriate Lyapunov functional, we show that the energy decay rate depends essentially on the properties of the relaxation function. As a consequence, classical decay rates such as exponential and polynomial decay as well as more general rates, are recovered as special cases of our approach.
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Copyright (c) 2026 Bouchelil Dounia, Lekdim Billal (Author)
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