A boundary layer approach to creeping waves. (December 2018)

• Record Type: Journal Article
• Authors: Matkowsky, B.J.
• Is Part Of: Applied mathematics letters. Volume 86(2018)
• Page Start: 320
• Page End: 325
• Publication Date: 2018-12
• Subjects: Wavelengths; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.07.011
• Languages: English
• ISSNs: 0893-9659

Abstract

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 = 2 π λ, 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.