Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data

DOI10.1090/S1061-0022-2011-01175-6zbMath1230.35057OpenAlexW2017377724MaRDI QIDQ3104489

S. Yu. Dobrokhotov, Brunello Tirozzi, Vladimir E. Nazaikinskii

Publication date: 14 December 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2011-01175-6

zbMATH Keywords

run-upwave frontsingular Lagrangian manifoldMaslov's canonical operator

Mathematics Subject Classification ID

Asymptotic expansions of solutions to PDEs (35C20) Initial value problems for second-order hyperbolic equations (35L15) Geometric optics (78A05)

Related Items (9)

On an elliptic operator degenerating on the boundary ⋮ Fock Quantization of Canonical Transformations and Semiclassical Asymptotics for Degenerate Problems ⋮ Two-fluid picture of supercritical phenomena ⋮ Method for the analysis of long water waves taking into account reflection from a gently sloping beach ⋮ Abnormal dispersion of fundamental Lamb modes in FG plates. II: Symmetric versus asymmetric variation ⋮ Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\) ⋮ Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data ⋮ New construction of classical thermodynamics and UD-statistics ⋮ Maslov's canonical operator for degenerate hyperbolic equations

Cites Work

• Geometric asymptotics for a degenerate hyperbolic equation
• Representations of rapidly decaying functions by the Maslov canonical operator
• Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations
• Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations
• Simple asymptotic solution of the Cauchy-Poisson problem for head waves
• Localized solutions of one-dimensional non-linear shallow-water equations with velocity $ c=\sqrt x$
• Focused tsunami waves
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