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On a free boundary problem for the equations of tidal motions

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  26 February 2010

Bui An Ton
Bui An Ton
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada.
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Extract

The purpose of this paper is two-fold, (i) to establish the existence of a unique local solution (in time) of an initial boundary-value problem for the tidal equations in bay areas and inlets, and (ii) to show the existence of a time-periodic solution of the equations when the tide raising force satisfies a condition involving the amplitude of the force, the depth of the sea and the domain considered.

MSC classification

Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 222 - 254
Copyright
Copyright © University College London 1983

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References

1.Bennett, A. F. and Kloeden, P. E.. The simplified quasigeostrophic equations: existence and uniqueness of strong solutions. Mathematika, 27 (1980), 287–311.CrossRefGoogle Scholar
2.Bennett, A. F. and Kloeden, P. E.. The dissipative quasigeostrophic equations. Mathematika, 28 (1981), 265–285.CrossRefGoogle Scholar
3.Browder, F. E.. Existence and uniqueness theorems for solutions of nonlinear boundary-value problems. Proc. Symp. Appl. Math., 17 (1965), 24–49.CrossRefGoogle Scholar
4.Duff, G. F. D.. Mathematical problems of tidal energy. Proc. Int. Congress oj Math. Vancouver (1974), Vol. 1, 87–94.Google Scholar
5.Dronskers, J. J.. Tidal computations in rivers and coastal waters (North Holland Publishing Co. Amsterdam, 1964).Google Scholar
6.Kanayama, H. and Ohtsuka, K.. Finite element analysis on the tidal current and COD distribution in Mikawa bay. Coastal Engineering Japan, 21 (1978), 157–171.CrossRefGoogle Scholar
7.Ladyzenskaya, O. A. and Solonnikov, V. A.. Unique solvability of an initial boundary-value problem for viscous incompressible nonhomogeneous fluids. Soviet Math., 10 (1978), 697.CrossRefGoogle Scholar
8.LeBlond, P. and Mysak, L. A.. Waves in the ocean (Elsevier Oceanographic services, Amsterdam, Oxford and New York, 1978).Google Scholar
9.Lions, J. L.. Quelques méthodes de resolution des problemes aux limites nonlineaires (Dunod, Paris, 1969).Google Scholar
10.Peetre, J.. Mixed problems for higher order elliptic equations in two variables (I), (II). Annali Scuola Norm. Pisa, 15 (1961), 337–353 and 17 (1963), 1-12.Google Scholar
11.Shamir, E.. Mixed boundary-value problems for elliptic equations in the plane. The Lp-theory. Annali Scuola Norm. Pisa, 17 (1963), 117–139.Google Scholar
12.Solonnikov, V. A.. Solvability of a problem on the motion of a viscous incompressible fluid bounded by a free surface. Math. USSR Izvestia, 11 (1977), 1323–1358.CrossRefGoogle Scholar
13.Ton, B. A.. Existence and uniqueness of a classical solution of an initial boundary-value problem of the theory of shallow waters. SIAM J. Math. Analysis, 12 (1981), 229–241.CrossRefGoogle Scholar
14.Ton, B. A.. On a free boundary problem for an inviscid incompressible fluid. Nonlinear Analysis, 6 (1982), 335–347.CrossRefGoogle Scholar
15.Ton, B. A.. On a free boundary problem for an inviscid incompressible fluid in a bounded region. To appear.Google Scholar
16.Visik, M. I. and Agranovich, M. S.. Elliptic problems with a parameter and parabolic problems of general type. Russian Math. Surveys 19 (1964), 53–159.Google Scholar