Results 241 to 250 of about 6,306,823 (285)

On the weak solutions to a shallow water equation

Communications on Pure and Applied Mathematics, 2000
The authors obtain the existence of global-in-time weak solutions to the Cauchy problem for a one-dimensional formally integrable shallow-water equation of Camassa-Holm type. First, for an approximate viscous problem they establish uniform in viscosity energy estimates for the solution and its gradient.
Xin, Zhouping, Zhang, Ping
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The shallow water equations

Journal of Engineering Mathematics, 1970
In this paper a set of exact nonlinear equations is derived for gravity flows. By assuming the flow to be shallow and assuming the vertical acceleration to be small these equations reduce to the classical equations for long waves in shallow water.
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Dispersive Nonlinear Shallow‐Water Equations

Studies in Applied Mathematics, 2009
A set of dispersive and hyperbolic depth‐averaged equations is obtained using a hyperbolic approximation of a chosen set of fully nonlinear and weakly dispersive Boussinesq‐type equations. These equations provide, at a reasonably reduced cost, both a physically sound description of the nearshore dynamics and a complete representation of dispersive and ...
Antuono, M., Liapidevskii, V., Brocchini, M.   +2 more
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An implicit wave equation model for the shallow water equations

Advances in Water Resources, 1984
In this paper an implicit numerical solution procedure for the shallow water equations is presented. It achieves efficiency through replacement of decompositions of a time-varying matrix by back substitutions for the solution of the equation system.
Ingemar P. E. Kinnmark, William G. Gray
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Wave Breaking for a Nonlinear Shallow Water Equation

Journal of Mathematical Fluid Mechanics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Jianmin, Yang, Shaojie
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The shallow-water equations

2009
We now enter the realm of hyperbolic equations. Instead of starting with an introduction to numerical methods for hyperbolic equations in general, we prefer to begin by plunging into the particular case of the shallow-water equations. Other hyperbolic equations will be considered in Chapters 9 and 10.
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Analytic solutions to the shallow water equations

Physical Review E, 2005
Analytic, two-dimensional steady-state solutions to the rotating shallow water equations over variable topography are derived, by exploiting a drastic simplification of the equilibrium problem that occurs for nondivergent flows. For such flows, the equilibrium system decouples, and the cross-stream component of the momentum equation formally reduces to
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Normalized shallow water equations

Moscow University Physics Bulletin, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elizarova, T. G., Afanasieva, M. V.
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A shallow water equation on the circle

Communications on Pure and Applied Mathematics, 1999
The purpose of this paper is to study the spatially periodic case of the shallow water equation \[ \partial v/\partial t+ v\partial t/\partial x+\partial p/\partial x= 0\tag{1} \] in which the ``pressure'' \(p\) is \((1- d^2/dx^2)^{-1}(v^2+{1\over 2} v^{\prime 2})\). The equation has been much studied in recent years, starting with \textit{R.
Constantin, A., McKean, H. P.
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On ?The shallow water equations? By M. Shinbrot

Journal of Engineering Mathematics, 1972
The paper [1] above describes two steady shallow water flows which differ from the known flows of this type. It is suggested that the conditions imposed in obtaining these solutions are not consistent.
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