General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure (Q903229)

In this paper the authors study the uniform decay rates of the energy of the wave equation \[ u_{tt} + b(x) f(u_t) -\Delta u +\int_0^t g(t-s) \operatorname{div}(a(x)\nabla u(\cdot ,s)) ds =0 \] containing viscoelastic dissipation and a nonlinear frictional damping terms. If the localization terms \(a(x)\) and \(b(x)\) satisfy the condition \(a(x)+b(x)\geq \delta>0\) for each \(x \in \Omega\), then general decay rate estimates are derived in this paper.