Mathematical Behavior of Solutions of Fourth-Order Hyperbolic Equation with Logarithmic Source Term

Abstract

The main goal of this paper is to study for a fourth-order hyperbolic equation with logarithmic nonlinearity. We obtain several results: Firstly, by using Feado-Galerkin method and a logaritmic Sobolev inequality, we proved local existence of solutions. Later, we proved global existence of solutions by potential well method. Finally, we showed the decay estimates result of the solutions.