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

MSC:
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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References:
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[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
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[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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