Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 653215, 7 pages
doi:10.1155/2010/653215
Research Article

The Well-Posedness of the Dirichlet Problem in the Cylindric Domain for the Multidimensional Wave Equation

Serik A. Aldashev

Aktobe State University, AGU, Br. Zhubanov Str 263, Aktobe 030000, Kazakhstan

Received 26 October 2009; Accepted 29 April 2010

Academic Editor: Carlo Cattani

Copyright © 2010 Serik A. Aldashev. 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

In the theory of hyperbolic PDEs, the boundary-value problems with conditions on the entire boundary of the domain serve typically as the examples of the ill-posedness. The paper shows the unique solvability of the Dirichlet problem in the cylindric domain for the multidimensional wave equation. We also establish the criterion for the unique solvability of the equation.