Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach

DOI10.1134/S0001434617050066zbMath1372.35180OpenAlexW2623921046MaRDI QIDQ2401644

S. Yu. Dobrokhotov, Anton A. Tolchennikov, Vladimir E. Nazaikinskii

Publication date: 4 September 2017

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434617050066

zbMATH Keywords

trace theoremlocalized sourcemodified Maslov canonical operatornonstandard characteristicsrun-up on a shallow beachhigher-order transport equationsspatially localized initial data

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Hydrology, hydrography, oceanography (86A05) Stability and instability of geophysical and astrophysical flows (76E20)

Related Items (5)

Inverse problem for the nonlinear long wave runup on a plane sloping beach ⋮ Uniformization and semiclassical asymptotics for a class of equations degenerating on the boundary of a manifold ⋮ О решении одной обратной задачи для уравнений мелкой воды в бассейне с переменной глубиной ⋮ Fock Quantization of Canonical Transformations and Semiclassical Asymptotics for Degenerate Problems ⋮ Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\)

Cites Work

• Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I
• New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics
• Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation
• On the representation of localized functions in \(\mathbb R^2\) by the Maslov canonical operator
• The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary
• Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data
• Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach