Boukhatem, Yamna et Benabderrahmane, Benyattou, Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions, Acta mathematica Sinica. English series (Print) , 32(2), 2016, pp. 153-174
A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.