Behavior of solutions of wave equations with logarithmic source term

In the first chapter of this dissertation, according to available literature,the information about the history of hyperbolic type evolution equations were given. Also, the applications of this type problem in daily life and physics were discussed. In the second chapter, the results of several studies related to hyperbolic type equations with logarithmic source term were analyzed. In the third chapter, the basic definition, theorem, inequalities, methods and equation modeling which will be used in this dissertation were given. The fourth chapter consists of three subsections. In the first subsection of the fourth chapter, the global existence, blow up at infinity and decay results of the solutions for the Boussinesq equation with the nonlinear logarithmic source term were obtained. In the second subsection, global existence, exponential growth and decay of solutions for the p-Laplacian equation with logarithmic source term were obtained. In the third subsection, the decay and global existence of the solutions for higher order Kirchhoff system with logarithmic source term were studied.