On decay and blow-up of solutions for a system of equations

Abstract

ABSTRACT In this paper, we consider a system of two viscoelastic equations with Dirichlet boundary conditions. Under suitable conditions, we establish a general decay result of solutions. Moreover, we prove a blow-up result for certain solutions with negative initial energy. This result extends the earlier result obtained by Liu [Uniform decay of solutions for a quasilinear system of viscoelastic equations, Nonlinear Anal. TMA 71 (2009) 2257–2267], in which only the usual exponential and polynomial decay rates are considered.