Water-waves modes trapped in a canal by a near-surface rough body

DOI10.1002/zamm.201000042zbMath1375.76024arXiv0910.1065OpenAlexW2007952100MaRDI QIDQ3066308

Giuseppe Cardone, Tiziana Durante, Sergueï A. Nazarov

Publication date: 10 January 2011

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1065

zbMATH Keywords

eigenvaluesasymptotic analysistrapped modes

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Curved channels with constant cross sections may support trapped surface waves ⋮ Band-gap structure of the spectrum of the water-wave problem in a shallow canal with a periodic family of deep pools ⋮ Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation ⋮ A body traps as many water-wave modes in a symmetric channel as it wishes ⋮ Spectra of open waveguides in periodic media ⋮ Properties of the spectrum in the John problem on a freely floating submerged body in a finite basin ⋮ Asymptotic behaviour of the Steklov spectrum on dumbbell domains ⋮ The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides ⋮ Asymptotic expansions for eigenvalues of the Steklov problem in singularly perturbed domains ⋮ Estimate for a solution to the water wave problem in the presence of a submerged body

Cites Work

• Regular degeneration and boundary layer for linear differential equations with small parameter