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

2010

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DOI 10.1155/2010/653215
Data confidence 70 medium
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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.