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Abstract. A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of… (More)
We study the nonlinear viscoelastic wave equation
The initial boundary value problem for an integro-differential equation with nonlinear damping in a bounded domain is considered. The local existence and blow-up of solutions with positive initial energy are discussed under some conditions. Estimates of the lifespan of solutions are also given.