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