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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 831012, 17 pages
http://dx.doi.org/10.1155/2012/831012
Research Article

Mixed Initial-Boundary Value Problem for Telegraph Equation in Domain with Variable Borders

Dnepropetrovsk National University, Faculty of Mechanics and Mathematics, Pr. Gagarina 72, Dnepropetrovsk 49010, Ukraine

Received 13 March 2012; Revised 6 April 2012; Accepted 11 April 2012

Academic Editor: Burak Polat

Copyright © 2012 V. A. Ostapenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Mixed initial-boundary value problem for telegraph equation in domain with variable borders is considered. On one part of domain’s border are the boundary conditions of the first type, on other part of the boundary are set boundary conditions of the second type. Besides, the sizes of area are variable. The solution of such problem demands development of special methods. With the help of consecutive application of procedure of construction waves reflected from borders of domain, it is possible to obtain the solution of this problem in quadratures. In addition, for construction of the waves reflected from mobile border, it is necessary to apply the procedure specially developed for these purposes.