Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term

Abstract

Abstract This paper is concerned with the existence and exponential stability of the global solution to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping − Δ u t and logarithmic source term u l n | u | R 2 . We apply the potential well corresponding to the logarithmic nonlinearity. We prove the global weak solutions and the exponential stability for initial data in the set of stability created from the Nehari Manifold.