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In the theory of hyperbolic PDEs, the boundary-value problems with conditions onthe 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 domainfor the multidimensional wave equation. We also establish the criterion for the uniquesolvability of the equation

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