Abstract
The existence of solutions of the Helmholtz equation, exponentially decreasing with distance from a periodic boundary in the upper half-plane, is proved. These solutions exist for a special form of the boundary under the Dirichlet or Neumann boundary conditions. In either case, the boundary has the form of a chain of resonators joined with the upper half-plane by narrow splits. Bibliography: 7 titles.
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References
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 83–96.
Translated by V. Yu. Gotlib
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Gotlib, V.Y. Solutions of the helmholtz equation, concentrated near a plane periodic boundary. J Math Sci 102, 4188–4194 (2000). https://doi.org/10.1007/BF02673850
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DOI: https://doi.org/10.1007/BF02673850