Translator Disclaimer
2004 An initial-boundary-value problem for hyperbolic differential-operator equations on afinite interval
Sasun Yakubov, Yakov Yakubov
Differential Integral Equations 17(1-2): 53-72 (2004).

Abstract

In this paper we give, for the first time, an abstract interpretation of initial--boundary-value problems for hyperbolic equations such that a part of the boundary-value conditions contains also a differentiation of the time $t$ of the same order as the equations. Initial--boundary-value problems for hyperbolic equations are reduced to the Cauchy problem for a system of hyperbolic differential-operator equations. A solution of this system is not a vector function but one function. At the same time, the system is not overdetermined. We prove the well-posedness of the Cauchy problem, and for some special cases we give an expansion of a solution to the series of eigenvectors. As application we show, in particular, a generalization of the classical Fourier method of separation of variables.

Citation

Download Citation

Sasun Yakubov. Yakov Yakubov. "An initial-boundary-value problem for hyperbolic differential-operator equations on afinite interval." Differential Integral Equations 17 (1-2) 53 - 72, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1164.34458
MathSciNet: MR2035495

Subjects:
Primary: 34G10
Secondary: 35L20, 35L90

Rights: Copyright © 2004 Khayyam Publishing, Inc.

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.17 • No. 1-2 • 2004
Back to Top