| 1Kryvonos, Yu.G 2Selezov, IT 1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv 2Institute of Hydromechanics of the NAS of Ukraine, Kyiv |
| Dopov. Nac. akad. nauk Ukr. 2014, 9:40-43 |
| https://doi.org/10.15407/dopovidi2014.09.040 |
| Section: Information Science and Cybernetics |
| Language: Russian |
Abstract: A generalized model of sedimentation, which considers the evolution of sediments on the bottom surface with a finite velocity is presented. We investigate a singular degeneration of the generalized hyperbolic equation to the traditional equation in the class of generalized solutions. |
| Keywords: degeneration, hyperbolic equation, modeling |
1. Maxwell J. C. Phil. Trans. Roy. Soc., 1867, 157: 49–88. https://doi.org/10.1098/rstl.1867.0004
2. Vabishchevich P. N. BIT Number Math., 2013, 53, No 3: 755–778. https://doi.org/10.1007/s10543-013-0423-7
3. Selezov I. T., Kryvonos Yu. G. Cybernetics and Systems Analysis, 2013, 49, No 4: 569–577. https://doi.org/10.1007/s10559-013-9542-z
4. Selezov I. T. Wave hydraulic models as mathematical approximations. Proc. 22th Congress, Int. Association for Hydraulic Research (IAHR), Lausanne, 1987, Techn. Session B., 1987.
: 301–306.
5. Ignatov E. I., Robsman V. A. Voprosy geografii, No 119: Morskie berega, 1982: 40–54 (in Russian).
6. Zang H., Kahawita R. J. Hydraulic Reseach., 1988, 26, No 3: 323–342. https://doi.org/10.1080/00221688809499215
7. Hjelmfelt A. T. River bed degradation in the placeMissouri river loess hills. The 23rd Congress of Int. Association for Hydraulic Research (IAHR), Theme: Hydraulics and Environment. Proc. Technical Session B: Fluvial CityHydraulics, country-regionCanada, CityplaceOttawa, 21–25 August 1989. B-233 – B-239.
8. Schwartz L. M´ethodes math´ematiques pour les sciences physiques. – Paris: Hermann, 1961.
9. Mizohata S. The theory of partial differential equations, Tokyo, 1965.
10. Ladyzhenskaya O. A. Boundary-value problems of mathematical physics Moscow: Nauka, 1973 (in Russian).
11. Krivonos Yu. G., Selezov I. T. Dopov. Nac. akad. nauk Ukr., 2013, No 7: 37–41.
12. Selezov I. T. The concept of hyperbolicity in the theory of controlled dynamic systems. In Cybernetics and calculated. equipment. Iss. 1, Kyiv: Nauk. dumka, 1969: 131–137 (in Russian).
13. Selezov I., Volynski R. Wave refraction and sediment dynamics modeling in coastal zone, Kiev: SMP “AVERS”, 2013.
14. Rudyak V. Ya., Smagulov Sh. O. DAN USSR, 1980, 255, No 4: 801–804 (in Russian).
