Generalized solutions for inextensible string equations

Tezel, Yasemin Şengül 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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Official URL: http://dx.doi.org/10.1016/j.jde.2016.11.040


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
ID Code:33218
Deposited By:Yasemin Şengül Tezel
Deposited On:22 Aug 2017 14:12
Last Modified:04 Nov 2019 23:33

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