Uniform decay of solutions for a nonlinear viscoelastic wave equation with boundary dissipation (Q1757909)

Summary: We consider a nonlinear viscoelastic wave equation \[ u_{tt}(t) - k_0\Delta u(t) + \int^t_0 g(t - s)\text{div}(a(x)\nabla u(s))ds + b(x)u_t = f(u) \] with nonlinear boundary damping in a bounded domain \(\Omega\). Under appropriate assumptions imposed on \(g\) and with certain initial data, we establish the general decay rate of the solution energy which is not necessarily of exponential or polynomial type. This work generalizes and improves earlier results in the literature.