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Attractors of differential inclusions for models of the atmospheric and oceanic dynamics, containing multivalued functions

Keywords:

V.M. Ipatova


The paper provides a brief introduction to the theory of attractors of multivalued semiflows. We consider the autonomous differential inclusions for the quasi-geostrophic models of general circulation of the atmosphere and the ocean with a multivalued right-hand side. It is proved that these differential inclusions have compact invariant global attractors.
References:

  1. Ivanov G.E., Polovinkin E.S. Vtoroj poryadok sxodimosti algoritma vy'chisleniya czeny' linejny'x differenczial'ny'x igr // Doklady' Akademii nauk. 1995. T. 340. № 2. S. 151–154.
  2. Ivanov G.E., Polovinkin E.S. O sil'no vy'pukly'x linejny'x differenczial'ny'x igrax // Differenczial'ny'e uravneniya. 1995. T. 31. № 10. S. 1641–1648.
  3. Polovinkin E.S., Ivanov G.E., Balashov M.V., Konstantinov R.V., Xorev A.V. Algoritmy' chislennogo resheniya linejny'x differenczial'ny'x igr // Matematicheskij sbornik. 2001. T. 192. № 10. S. 95–122.
  4. Zaxarov V.K., Polovinkin E.S., Jashin A.D. Matematicheskaya model' gosudarstva // Doklady' Akademii nauk. 2007. T. 413. № 2. S. 158–162.
  5. Shamin R.V. Opisanie dinamiki voln na vode na osnove differenczial'ny'x vklyuchenij // Doklady' Akademii nauk. 2011. T. 438. № 4. S. 453–455.
  6. Ipatov D.E. Razreshimost' differenczial'nogo vklyucheniya dlya mnogoslojnoj modeli obshhej czirkulyaczii okeana s mnogoznachnoj pravoj chast'yu // Al'manax sovremennoj nauki i obrazovaniya. 2012. № 12–2. S. 52–55.
  7. Kapustyan O.V., Mel’nik V.S., Valero J., Yasinsky V.V. Global attractors of multi-valued dynamical systems and evolution equations without uniqueness. Kyiv: Naukova Dumka. 2008. 215 p.
  8. Polovinkin E.S. E'lementy' teorii mnogoznachny'x otobrazhenij. M.: MFTI. 1982. 127 s.
  9. Il'in A.A., Filatov A.N. Uravneniya Nav'e-Stoksa na dvumernoj sfere i ix odnoznachnaya razreshimost'. Ustojchivost' staczionarny'x reshenij // V sb.: Matematicheskaya fizika. L.: Izd. LGPI. 1987. S. 126–142.
  10. Skiba Ju.N. Matematicheskie voprosy' dinamiki vyazkoj barotropnoj zhidkosti na vrashhayushhejsya sfere. M.: OVM AN SSSR. 1989.
  11. Filatov A.N., Ipatova V.M. On globally stable difference schemes for the barotropic vorticity equation on a sphere // Russian Journal of Numerical Analysis and Mathematical Modelling. 1996. V. 11. № 1. P. 1–26.
  12. Filatov A.N., Ipatova V.M. Globally stable difference schemes for the barotropic vorticity equation with the almost-periodic right-hand side // Russian Journal of Numerical Analysis and Mathematical Modelling. 1996. V. 11. № 4. P. 287–302.
  13. Ipatova V.M. Ob attraktorax approksimaczij neavtonomny'x e'volyuczionny'x uravnenij // Matematicheskij sbornik. 1997. T. 188. № 6. S. 47–56.
  14. Lions Zh.-L. Nekotory'e metody' resheniya nelinejny'x kraevy'x zadach. M.: Mir. 1972.
  15. Lions Zh.-L., Madzhenes E'. Neodnorodny'e granichny'e zadachi i ix prilozheniya. M.: Mir. 1971.
  16. Bernier Ch. Existence of attractor for the quasi-geostrophic approximation of the Navier-Stokes equations and estimate of its dimension // Advances in Mathematical Sciences and Applications. 1994. V. 4. № 2. P. 465–489.
  17. Agoshkov V.I., Ipatova V.M. Razreshimost' zadachi usvoeniya danny'x al'timetrii v kvazigeostroficheskoj mnogoslojnoj modeli okeana // ZhVM i MF. 1997. T. 37. № 3. S. 355–367.
  18. Ipatova V.M. Uniform attractors of finite-difference schemes for the multilayer quasigeostrophic model of ocean dynamics // Russian Journal of Numerical Analysis and Mathematical Modelling. 2011. V. 26. № 2. P. 143–159.

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