A PROBLEM ON VIBRATION OF A BAR WITH UNKNOWN BOUNDARY CONDITION ON A PART OF THE BOUNDARY



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Abstract

In this paper, we study an inverse problem for hyperbolic equation. This problem arises when we consider vibration of a nonhomogeneous bar if one endpoint is fixed by spring but behavior of the other is unknown and is the subject to find. Overdetermination is given in the form of integral with respect to spacial variable. Unique solvability of this problem is proved under some conditions on data. The proof is based on a priori estimates in Sobolev space.

About the authors

A. B. Beylin

Samara State Technical University

Author for correspondence.
Email: morenov@ssau.ru
Russian Federation

L. S. Pulkina

Samara National Research University

Email: morenov@ssau.ru
Russian Federation

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Copyright (c) 1970 Beylin A.B., Pulkina L.S.

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