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Existence and Uniqueness of Weak Solutions for the Model Representing Motions of Curves Made of Elastic Materials

We consider the initial boundary value problem for the beam equation with the nonlinear strain. In our previous work this problem was proposed as a mathematical model for stretching and shrinking motions of the curve made of the elastic material on the plane. The aim of this paper is to establish uniqueness and existence of weak solutions. In particular, the uniqueness is proved by applying the approximate dual equation method.