General Decay and Blow-up Results for a Thermo-viscoelastic System with Logarithmic Nonlinearity

Abstract

This paper deals with a nonlinear thermo -viscoelastic system with logarithmic nonlinearity of the form on a bounded domain Ω⊂Rn. By using the modified potential-well method, we first show the global existence and the finite-time blow-up results of solutions. Further, we give explicit and general decay rates of the energy functional associated with the global solution under a general class of relaxation function g which includes exponential, logarithmic, and polynomial rates. Besides, the lower and upper bounds for the blow-up time are also studied.