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An initial- and boundary-value problem for a model equation for propagation of long waves. (English) Zbl 0444.35069

35Q99 Partial differential equations of mathematical physics and other areas of application
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35C15 Integral representations of solutions to PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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[1] Benjamin, T.B, Lectures on nonlinear wave motion, () · Zbl 0119.21503
[2] Benjamin, T.B; Bona, J.L; Mahony, J.J, Model equations for long waves in nonlinear dispersive systems, Philos. trans. roy. soc. London, 272, 47-78, (1972) · Zbl 0229.35013
[3] Bona, J.L; Bryant, P.J, A mathematical model for long waves generated by wavemakers in nonlinear dispersive systems, (), 391-405 · Zbl 0261.76007
[4] Bona, J.L; Pritchard, W.G; Scott, L.R, A comparison of laboratory experiments with a model equation for long waves, () · Zbl 0534.76024
[5] Bona, J.L; Smith, R, The initial-value problem for the Korteweg-de Vries equation, Philos. trans. roy. soc. London, 278, 555-604, (1975) · Zbl 0306.35027
[6] Hammack, J.L, A note on tsunamis: their generation and propagation in an Ocean of uniform depth, J. fluid mech., 60, 769-799, (1973) · Zbl 0273.76010
[7] Kakutani, T; Matsuuchi, K, Effect of viscosity on long gravity waves, J. phys. soc. Japan, 39, 237-246, (1975) · Zbl 1334.76018
[8] Medeiros, L.A; Menzala, G.Perla, Existence and uniqueness for periodic solutions of the Benjamin-Bona-Mahony equation, SIAM J. math. anal., 8, 792-799, (1977) · Zbl 0337.35004
[9] Medeiros, L.A; Miranda, M.Milla, Weak solutions for a nonlinear dispersive equation, J. math. anal. appl., 59, 432-441, (1977) · Zbl 0376.35011
[10] Peregrine, D.H, Calculations of the development of an undular bore, J. fluid mech., 25, 321-330, (1966)
[11] Showalter, R.E, Existence and representation theorems for a semilinear Sobolev equation in a Banach space, SIAM J. math. anal., 3, 527-543, (1972) · Zbl 0262.34047
[12] Showalter, R.E, Sobolev equations for nonlinear dispersive systems, Appl. anal., 7, 297-308, (1978) · Zbl 0387.34043
[13] Sobolev, S.L; Sobolev, S.L, Applications of functional analysis in mathematical physics, (), (1950), Izdat. Leningrad, Gos. Univ., Leningrad, English trans. · Zbl 0041.52307
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