### Abstract

We consider the eigenvalue problem for the Laplace operator in a two dimensional domain exterior to a smooth, closed convex curve C, on which the eigenfunctions are to vanish. Waves whose wavelengths λ are very small may be viewed as particles traveling along specific paths termed rays, along which the waves propagate. Small wavelengths λ correspond to large wavenumbers k=[Formula presented], which are the eigenvalues. Therefore, we restrict attention to the consideration of large eigenvalues. If the amplitude of the eigenfunctions is appreciable only in a thin region attached to the boundary and is negligibly small beyond the layer, they correspond to creeping waves. We employ a boundary layer approach to the problem.

Original language | English (US) |
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Pages (from-to) | 320-325 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 86 |

DOIs | |

State | Published - Dec 2018 |

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### Keywords

- Wavelengths

### ASJC Scopus subject areas

- Applied Mathematics