Zayıf Disipatif Camassa-Holm Denkleminin Patlaması Olayı Üzerine

Abstract

This study is devoted to the blow up solutions of the Cauchy problem for the weakly dissipative Camassa-Holm equation. In introductory chapter, the problem we studied has been introduced and other authors' studies done on the type of similar problems are mentioned. In the second chapter, general and specific informations which were used in this study are given. In the third chapter, Cauchy problem for the weakly dissipative Camassa-Holm equation is considered. In this chapter, our study has been investigated in two sub-sections as local existence and uniqueness and constant commitment of solution to k dispersive coefficient. In the forth chapter, under certain conditions global existence for problem discussed in Sobolev space has been examined in two sub-sections for situations where k dispersive coefficient is 0 and different from 0. In the fifth chapter, the sufficient conditions which guarantee the blow up of the solution of the problem under consideration in finite time considered.