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
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.