Blow-up theorems for nonlinear evolutionary PDE`s

Abstract

Bu tezde dogrusal olmayan parabolik, hiperbolik, Schrödinger denklemleri ile termoelastik denklem sistemleri icin Cauchy problemi ve baslangıc-sınır degeri problemlerinin cozumlerinin sonlu zamanda patlaması problemini inceliyoruz.

In this thesis we will study problems of blow-up of solutions of the Cauchy problem and initial-boundary value problems for nonlinear parabolic, nonlinear hyperbolic, nonlinear Schrödinger equations and systems of thermoelasticity type. First we study results on blow-up of solutions for nonlinear heat equation, nonlinear wave equation and nonlinear Schrödinger equation obtained in last years by using the energy methods. Then, we investigate the problem of blow-up and global non-existence of the solution to the initial boundary value problem for a nonlinear thermoelastic system.