Generalized solutions for inextensible string equations
Şengül, 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)
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.
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