Asymptotic behaviour and blow up of the solution of the inverse with memory term problem for nonlinear hyperbolic partial differential equations

This thesis consists of five chapters. In the first chapter, notations and main equalities used in the thesis are given. Furthermore, Generalized Concavity Lemma and it's proof are given. In addition to, definitions and theorems of Sobolev Spaces, Sobolev-Poincare Inequality and proof of Poincare Inequality are given. In the second chapter, inverse problem examples are given. In the third chapter, asymptotic behaviour of the solution of the inverse with memory term problem for nonlinear hyperbolic partial differential equations is examined. In the fourth chapter, blow up of the solution of the inverse with memory term problem for nonlinear hyperbolic partial differential equations is examined. Finally in the fifth chapter, the results and suggestions are stated gained through the study of thesis. Keywords: Inverse problem, Asymptotic stability, Nonlinear hyperbolic equations, Blow up, Memory term