Generalized solutions for inextensible string equations

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Şengül Tezel, Yasemin and Vorotnikov, Dmitry (2017) Generalized solutions for inextensible string equations. Journal of Differential Equations, 262 (6). pp. 3610-3641. ISSN 0022-0396 (Print) 1090-2732 (Online)

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Abstract

We study the system of equations of motion for inextensible strings. This system can be recast into a discontinuous system of conservation laws as well as into the total variation wave equation. We prove existence of generalized Young measure solutions with non-negative tension after transforming the problem into a system of conservation laws and approximating it with a regularized system for which we obtain uniform estimates of the energy and the tension. We also discuss sufficient conditions for non-negativity of the tension for strong solutions.
Item Type: Article
Uncontrolled Keywords: inextensible string, generalized Young measure, whip, 1-Laplacian, principle of least action, conservation law
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Yasemin Şengül Tezel
Date Deposited: 22 Aug 2017 14:12
Last Modified: 26 Apr 2022 09:48
URI: https://research.sabanciuniv.edu/id/eprint/33218

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