On Behavior of Solutions for Nonlinear Klein–Gordon Wave Type Models with a Logarithmic Nonlinearity and Multiple Time-Varying Delays

Abstract

In this paper, we study the existence and exponential stability of solutions to a class of nonlinear delay Klein–Gordon wave type models on a bounded domain. Such models include multiple time-varying delays, frictional damping, and nonlinear logarithmic source terms. After showing the local existence result of the solutions using Faedo–Galerkin’s method and logarithmic Sobolev inequality, the global existence is analyzed. Then, under some appropriate conditions, energy decay estimates and exponential stability results of the global solutions are investigated.

Keywords

• nonlinear Klein–Gordon equation
• multiple time-varying delays
• nonlocal equation
• logarithmic source term
• asymptotic behavior
• energy decay