Bui An Ton Initial-value problems for the Boussinesq equations of water waves. (English) Zbl 0441.76011 Nonlinear Anal., Theory Methods Appl. 4, 15-26 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35G25 Initial value problems for nonlinear higher-order PDEs Keywords:initial-value problems; Boussinesq equations; long water waves; flat bottom; asymptotic expansion; time-dependent Cauchy-Poisson problem; non- coercive non-linear equations; Sobolev-Galpern type PDFBibTeX XMLCite \textit{Bui An Ton}, Nonlinear Anal., Theory Methods Appl. 4, 15--26 (1980; Zbl 0441.76011) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.