Abstract
The surface and subsoil waters joint motion problem is considered. Conjugate conditions for the Euler’s and Darcy’s equations are imposed. The boundary value problem is reduced to a system of integro-differential equations. A local existence and uniqueness theorem is proved in a scale of Banach spaces of analytic functions.
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References
Ovsiannikov L.V., Makarenko N.I., Nalimov V.I., et al. Nonlinear problems of surface and internal wave theory. Novosibirsk, Nauka, 1985 (in Russian).
Ladyzhenskaya O.A., Solonnikov V.A., Ural’tseva N.N. Linear and quasilinear equations of parabolic type. Trans.Math. Monographs 23, Amer. Math. Soc., Providence, R.I., 1968.
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© 1992 Springer Basel AG
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Shelukhin, V.V. (1992). The Justification of the Conjugate Conditions for the Euler’s and Darcy’s Equations. In: Antontsev, S.N., Khludnev, A.M., Hoffmann, KH. (eds) Free Boundary Problems in Continuum Mechanics. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8627-7_33
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DOI: https://doi.org/10.1007/978-3-0348-8627-7_33
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9705-1
Online ISBN: 978-3-0348-8627-7
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