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A model for the two-way propagation of water waves in a channel

  • Jerry L. Bona (a1) and Ronald Smith (a1)


Global existence, uniqueness and regularity of solutions and continuous dependence of solutions on varied initial data are established for the initial-value problem for the coupled system of equations

This system has the same formal justification as a model for the two-way propagation of (one-dimensional) long waves of small but finite amplitude in an open channel of water of constant depth as other versions of the Boussinesq equations. A feature of the analysis is that bounds on the wave amplitude η are obtained which are valid for all time.



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(10)Peregrine, D. H.Discussion of the paper ‘A numerical simulation of the undular hydraulic jump’ by M. B. Abbott and G. S. Rodenhuis. Journal of Hydraulic Research 12 (1974), 141.
(11)Yosida, K.Functional analysis (3rd edition, Springer-Verlag, 1971).


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