MSc Thesis Defense: Burak Kardaş, CAUCHY PROBLEM FOR A HIGHLY NONLINEAR CAMASSA-HOLM TYPE EQUATION, Date & Time: June 23, 2026 – 11:00 AM, Place: FENS 2019

CAUCHY PROBLEM FOR A HIGHLY NONLINEAR CAMASSA-HOLM TYPE

EQUATION

Burak Kardaş
Mathematics, MSc Thesis, 2026

Thesis Jury

     Asst. Prof. Nilay Duruk Mutlubaş

  Prof. Nihat Gökhan Göğüş

Prof. Hüsnü Ata Erbay

Date & Time: June 23rd, 2026  – 11:00 AM

Place: FENS 2019

 

Keywords :

Generalized Camassa-Holm equation, Kato’s semigroup approach,

Local well-posedness, Finite time blow-up

Abstract

This thesis investigates existence and blow-up properties of a Camassa-Holm type equation. In particular, we analyze the structure of the equation under specified initial conditions. We characterize it and compare it to some more well known partial differential equations like standard Camassa-Holm, Degasperis-Procesi and Novikov equations. By applying Kato’s semigroup approach for quasi-linear evolution equations, we establish the well-posedness of the associated Cauchy problem within the appropriate Sobolev spaces, as well as the uniqueness of its solutions. Additionally, we prove finite time blow-up conditions depending on the parameters of the equation and the initial data.