Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 547-567

On some boundary value problems for a class of hyperbolic systems of second order in conic domains

S. Kharibegashvili

A. Razmadze Mathematical Institute, Department of Mathematics and Physics, Georgian Academy of Sciences, Tbilisi 0193, Georgia

Received 16 December 2003

Copyright © 2005 S. Kharibegashvili. 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.


For one class of hyperbolic systems of second order, we consider multidimensional versions of the Darboux problem in conic domains. A priori estimates of solutions of these problems are obtained. The existence of a solution of the Darboux problems is proved under the supplementary conditions imposed on the coefficients of the system, when the data support of the problem is of temporary type.