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Initial-value problems for the Boussinesq equations of water waves. (English) Zbl 0441.76011


MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35G25 Initial value problems for nonlinear higher-order PDEs
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References:

[1] Benjamin, T. B., Nonlinear wave motion, Lectures in Appl. Math. Am. math. Soc.. Lectures in Appl. Math. Am. math. Soc., Am. math. Soc., 15, 3-47 (1974)
[2] Whitham, G. B., Linear and Nonlinear Waves (1974), J. Wiley: J. Wiley New York · Zbl 0373.76001
[3] Showalter, R. E.; Ting, T. W., Pseudo parabolic partial differential equations, Siam J. Math. Analysis, 1, 1-26 (1970) · Zbl 0199.42102
[5] Lions, J. L., Equations Differentielles Operationnelles et Problemes aux Limites (1961), Springer: Springer New York · Zbl 0098.31101
[6] Ebin, D. G.; Marsden, J. E., Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math., 97, 102-163 (1970) · Zbl 0211.57401
[7] Aubin, J. P., Un théorème de compacité, C. r. hebd. Séanc. Acad. Sci. Paris, 245, 5042-5044 (1963) · Zbl 0195.13002
[8] Benjamin, T. B.; Bona, J. L.; Mahony, J. J., Model equations for long waves in nonlinear dispersive systems, Phil. Trans. R. Soc. Lond. Ser. A, 272, 47-78 (1972) · Zbl 0229.35013
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