On the Existence of Solutions for Inextensible String Equations

Ayk Telciyan
Mathematics, MSc. Thesis, 2018

Thesis Jury

Asst. Prof. Dr. Yasemin Şengül (Thesis Advisor)

Asst. Prof. Dr. Nilay Duruk Mutlubaş

Assoc. Prof. Dr. Gülçin Mihriye Muslu (İTÜ)

Date & Time: 31 July, 2018 –  2 PM

Place: FENS - G029

Keywords : inextensible string, hyperbolic conservation law, traveling waves, periodic boundary conditions, existence of solutions

Abstract

In this thesis, we analyze existence of solutions for inextensible string equations. In particular, we have results in two directions.

On one hand, we find explicit traveling wave solutions for a system of hyperbolic conservation laws resulting from inextensible string equations via suitable change of variables. Then, we relate this solution with entropy and shock-wave solutions for which an established theory already exists.

On the other hand, we consider the problem with periodic boundary conditions and show local existence of solutions using well-studied results related to the wave equation.