Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions

Abstract

In the present work, we establish a blow-up criterion for viscoelastic wave equations with nonlinear damping, logarithmic source, delay in the velocity, and acoustic boundary conditions. Due to the nonlinear damping term, we cannot apply the concavity method introduced by Levine. Thus, we use the energy method to show that the solution with negative initial energy blows up after finite time. Furthermore, we investigate the upper and lower bounds of the blow-up time.

Keywords

• blow-up
• viscoelastic equation
• logarithmic nonlinearity
• time delay
• acoustic boundary condition
• nonlinear dissipation
• 35l05
• 35l70
• 35b44