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Journal Nonlinear World №3 for 2013 г.
Article in number:
0Solvability of an inviscid model of tides
Keywords:
equations of hydrodynamics
shallow water equations
the model of tides
initial-boundary value problem
existence and uniqueness of the solution
Authors:
V.M. Ipatova
Abstract:
An inviscid model of tides with a nonlinear term of bottom friction is considered. Assumed that a value of the normal component of a velocity vector is given on the boundary. We prove the existence and uniqueness of the solution of the initial-boundary value problem on a finite time interval.
Pages: 164-171
References
- Agoshkov V.I., Ipatova V.M. Razreshimost odnojj zadachi variacionnogo usvoenija dannykh nabljudenijj // DAN. 1998. T. 360. № 4. S. 439-441.
- Agoshkov V.I., Ipatova V.M. Razreshimost zadachi usvoenija dannykh nabljudenijj v trekhmernojj modeli dinamiki okeana // Differencialnye uravnenija. 2007. T. 43. № 8. S. 1064-1075.
- Marchuk G.I., Agoshkov V.I., Ipatova V.M. Teorija razreshimosti nachalno-kraevykh zadach i zadach assimiljacii dannykh dlja osnovnykh uravnenijj okeana // Trudy MFTI. 2011. T. 3. № 1. S. 93-101.
- Ipatova V.M. O ravnomernykh attraktorakh javnykh approksimacijj // Differencialnye uravnenija. 2011. T. 47. № 4. S. 574-583.
- Ipatova V.M. Zadacha inicializacii dlja modeli obshhejj cirkuljacii atmosfery // Trudy MFTI. 2012. T. 4. № 2. S. 121-130.
- Ipatova V.M. Ob attraktore nejavnojj proekcionno-raznostnojj skhemy dlja dvukhslojjnojj modeli obshhejj cirkuljacii atmosfery s zavisjashhejj ot vremeni pravojj chastju // Nelinejjnyjj mir. 2012. T. 10. № 8. S. 515-527.
- Ipatova V.M., Ipatov D.E. Reshenie zadach ob opredelenii koehfficientov dlja trekhmernojj modeli gidrotermodinamiki okeana // Almanakh sovremennojj nauki i obrazovanija. 2011. № 9. S. 25-29.
- Agoshkov V.I., Ipatova V.M. Solvability of the altimeter data assimilation problem in the quasi-geostrophic multilayer model of ocean circulation // Computational Mathematics and Mathematical Physics. 1997. T. 37. № 3. S. 355-366.
- Agoshkov V.I., Ipatova V.M.Existence theorems for a three-dimensional ocean dynamics model and a data assimilation problem //Doklady Mathematics. 2007. V. 75. № 1. P. 28-30.
- Ipatova V.M. Solvability of the ocean hydrothermodynamics problem under a nonlinear state equation // Russian Journal of Numerical Analysis and Mathematical Modelling. 2008. V. 23. № 2. P. 185-196.
- Volcinger N.E., Klevannyjj K.A., Pelinovskijj E. N. Dlinnovolnovaja dinamika pribrezhnojj zony. L.: Gidrometeoizdat. 1989.
- Nekrasov A.V. EHnergija okeanskikh prilivov. L.: Gidrometeoizdat. 1990.
- Marchuk G.I., Kagan B.A. Okeanskie prilivy. Matematicheskie modeli i chislennye ehksperimenty. L.: Gidrometeoizdat. 1977.
- Girault V., Raviart P. Finite element methods for Navier-Stokes equations. Berlin-Heidelberg-New York-Tokyo: Springer-Verlag, 1986.
- Lions ZH.-L. Nekotorye metody reshenija nelinejjnykh kraevykh zadach. M.: Mir. 1972.