### 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 1 2018 |

### Fingerprint

### Keywords

- Wavelengths

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

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*Applied Mathematics Letters*, vol. 86, pp. 320-325. https://doi.org/10.1016/j.aml.2018.07.011

**A boundary layer approach to creeping waves.** / Matkowsky, Bernard J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A boundary layer approach to creeping waves

AU - Matkowsky, Bernard J

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Wavelengths

UR - http://www.scopus.com/inward/record.url?scp=85050618490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050618490&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2018.07.011

DO - 10.1016/j.aml.2018.07.011

M3 - Article

VL - 86

SP - 320

EP - 325

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -