Asymptotics of the solutions of the one-dimensional nonlinear system of equations of shallow water with degenerate velocity

DOI10.1134/S0001434612110090zbMath1278.35180OpenAlexW2030189886MaRDI QIDQ1946428

D. S. Minenkov

Publication date: 15 April 2013

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

Full work available at URL: https://doi.org/10.1134/s0001434612110090

zbMATH Keywords

Cauchy problemHankel transformSchwartz spaceCarrier-Greenspan transformationDuhamel integralnonlinear system of equations of shallow water

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30)

Related Items (6)

Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach ⋮ Asymptotics of long nonlinear propagating waves in a one-dimensional basin with gentle shores ⋮ Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms ⋮ Two-fluid picture of supercritical phenomena ⋮ 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

Uses Software

• DLMF

Cites Work

• Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I
• Geometric asymptotics for a degenerate hyperbolic equation
• NIST digital library of mathematical functions
• Water waves of finite amplitude on a sloping beach
• Localized solutions of one-dimensional non-linear shallow-water equations with velocity $ c=\sqrt x$

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