Abstract
Long wave approximation [1] of free boundary problem, describing water waves is considered. In the case of vortical flow corresponding problem may be reduced to Cauchy problem to system of integrodifferential equations [2]. Notion of hyperbolicity is introduced and hyperbolicity conditions for system of long waves are found. Discretization of the problem, based on the characteristic properties of equations is proposed.
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References
Benney, D. J., Some properties of long waves, Stud. Appl. Math. 52 (1973), 45–69.
Zakharov, V. E., Benney equations and quasiclassical approximation in inverse problem method, E.glish transl. in Functional Anal. Appl. 14 (1980), Funktsional. Anal. i Prilozhen 14, No. 2 (1980), 15–24.
Teshukov, V. M., On the hyberbolicity of long wave equations,Soviet Math. Dokl. 32, No. 2 (1985), 469–673.
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© 1991 Springer Basel AG
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Teshukov, V.M. (1991). Long wave approximation for vortex free boundary flows. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_37
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DOI: https://doi.org/10.1007/978-3-0348-5715-4_37
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5717-8
Online ISBN: 978-3-0348-5715-4
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