Electron. J. Diff. Eqns., Vol. 2001(2001), No. 76, pp. 1-8.

Existence of solutions for one-dimensional wave equations with nonlocal conditions

Sergei A. Beilin

Abstract:
In this article we study an initial and boundary-value problem with a nonlocal integral condition for a one-dimensional wave equation. We prove existence and uniqueness of classical solution and find its Fourier representation. The basis used consists of a system of eigenfunctions and adjoint functions.

Submitted August 21, 2001. Published December 10, 2001.
Math Subject Classifications: 35L99, 35L05, 35L20.
Key Words: Mixed problem, non-local conditions, wave equation.

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Sergei A. Beilin
Department of Mathematics, Samara State University
1, Ac.Pavlov st.
443011 Samara Russia
e-mail: sbeilin@narod.ru, awr@ssu.samara.ru
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