Generalized solutions for inextensible string equations

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.