Blow-up phenomena for a singular nonlocal viscoelastic problem with logarithmic nonlinearity

Abstract

This article deals with the blow-up phenomena for a singular nonlocal viscoelastic equation with logarithmic nonlinearity subject to nonlocal boundary conditions u(α,t)=0 and ∫0αxu(x,t)dx=0. Under the three different initial energy levels, we established the finite time blow-up criterion, and then give the upper bounds for blow-up time T∗ depending on the sign and range of initial energy E(0).