On the Existence of Solutions for Inextensible String Equations
Mathematics, MSc. Thesis, 2018
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
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.