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Generalized solutions for inextensible string equations

Sengul, Yasemin and Vorotnikov, Dmitry 2017. Generalized solutions for inextensible string equations. Journal of Differential Equations 262 (6) , pp. 3610-3641. 10.1016/j.jde.2016.11.040

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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
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0022-0396
Last Modified: 01 Dec 2021 15:45

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