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- W2519980213 abstract "UDC 517 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. The Helmholtz equation with Dirichlet or Neumann boundary condition in the domains f~ shown in Fig. la-c is considered. Without loss of generality, the value of the x period of the boundary is taken to be equal to 27r with two resonators on a period. We prove the existence of a solution of (1) satisfying the periodicity condition u(x + 27r) = u(x) in the functional class L2 on the x period. This is established by the method of [3] under the assumption that the parameter d (the half-length of a split) is small." @default.
- W2519980213 created "2016-09-23" @default.
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- W2519980213 date "2000-01-01" @default.
- W2519980213 modified "2023-09-23" @default.
- W2519980213 title "SOLUTIONS OF THE H ELMHOLTZ E QUATION, C ONCENTRATED NEAR A PLANE P ERIODIC B OUNDARY" @default.
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