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Scientific Journal of Samarkand University

Abstract

The initial-boundary value problem for systems of viscous two-fluid media with the same pressure in components is considered. Using the trial function method proposed in the works of Pohozhaev and Mitidieri, the influence of boundary and initial conditions on the appearance and time of destruction of solutions of these problems is investigated.

First Page

19

Last Page

25

References

1. Loysyanskiy L. G. Mexanika jidkosti i gaza. M.: Nauka, 1978. 2. SHlixting G. Teoriya pogranichnogo sloya. M.: Nauka, 1974.3. Pohozaev S.I. Critical nonlinearities in partial differential equations // Milan J. Math. — 2009. — N 1. — P. 127–150. 4. Savin V. O., Sciunzi B., Valdinoci E. Flat level set regularity of p-Laplace phase transition // Memoirs AMS. — 2006. — V. 182. — P. 1–144. 5. Constantin A., Escher J. Wave breaking for nonlinear nonlocal shallow water equations // Acta Math., 1998, v. 181 (2), pp. 229-243. 6. Zhou Y. Wave breaking for a shallow water equation // Nonlinear Anal. Theory, MethodsAppl., 2004, v. 57(1), pp. 137-152. 7. Mitidieri E., Poxojaev S.I. Apriornye otsenki i otsutstvie resheniy nelineynyx uravneniy i neravenstv v chastnyx proizvodnyx // Tr. MIAN, 2001, t. 234, Nauka, M., s. 3-383. 8. Poxojaev S.I. O kvaziinvariantax Rimana // Matem. sb., 2011, t. 202, No. 6, s. 111-132 9. Poxojaev S.I. O nekotoryx vesovyx tojdestvax dlya resheniy obobshennyx uravneniy Kortevega-de Friza // Matem. zametki, 2011, t. 89, No. 3, s. 393-409. 10. Poxojaev S.I. Ob otsutstvii globalnyx resheniy uravneniya Kortevega-de Friza // Uravneniya v chastnyx proizvodnyx, SMFN, No. 39, RUDN, M., 2011, s. 141-150. 11. Galaktionov V.A., Mitidieri E., Pohozhaev S.I. On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations // Nonlinear Anal., 2009, v. 70, No. 8 pp. 2930-2952. 12. Poxojaev S.I. Ob otsutstvii globalnyx resheniy nekotoryx nachalno-kraevyx zadach dlya uravneniya Kortevega-de Friza // Differens. uravneniya, 2011, t. 47, No. 4, s. 493-498. 13. Xolmurodov A.E., Dilmurodov N. Matematicheskoe modelirovanie odnoy nelineynoy dinamicheskoy sistemy, voznikayushey v nasyshennoy jidkostyu poristoy srede// Nauchnyy jurnal “Problemy vыchislitelnoy i prikladnoy matematiki” , TUIT, № 2(8) 2017, C. 5661. 14. YUshkov E.V. O razrushenii resheniya v sistemax tipa Kortvega-de Friza // TMF, 2012, t. 173, No. 2, s.197-206.\bibitem{15} Dobroxotov S.YU., SHafarevich A. I. O povedenii na beskonechnosti polya skorostey nesjimaemoy jidkosti // Mexanika jidkosti i gaza, 1996, t. 31, No. 4, s. 38-42. 15. YUshkov E.V. O razrushenii resheniy uravneniy gidrodinamicheskogo tipa pr spetsialnyx granichnyx usloviyax // Diff. uravneniya, 2012, t. 48, No. 9, s. 1234-1239. 16. Lai S., Wu Y. Global solutions and blow-up phenomena to a shallow water equation // J. Differ. Equ., 2010, v. 249, No. 3, pp. 693-706. 17. Kholmurodov A, Dilmuradov.N. Additional Conservation Laws for Two-Velocity Hydrodynamics Equations with the Same Pressure in Components// Research Inventy: International Journal of Engineering And Science Vol.7, Issue 1 (January 2017), PP -39-45, Issn (e): 2278-4721, Issn (p):2319-6483, www.researchinventy.com 18. Imomnazarov X.X., Imomnazarov SH.X., Mamatkulov M.M. CHernyx G.G. Fundamentalnoe reshenie dlya statsionarnogo uravneniya dvuxskorostnoy gidrodinamiki s odnim davleniem // SibJIM, 2014, t. 17, № 4(60), s. 60-66. 19. Imomnazarov Kh.Kh., Imomnazarov Sh.Kh., Mamatqulov M.M., Chernykh E.G. The fundamental solution of the stationary two-velocity hydrodunamics equation with one pressure // Bull. Of the Novosibirsk Computing Center, series: Mathematical Modeling in Geophysics, Novosibirsk, 2014, № 17, pp.5-12. 20. Gudovich I.S., Kreyn S.G., Kulikov I.M. Kraevye zadachi dlya uravneniy Maksvella // Doklady AN SSSR, 1972, t. 207, № 2, s. 321-324. 21. Urev M.V., Imomnazarov X.X., Jian-Gan Tan Kraevaya zadacha dlya odnoy pereopredelennoy statsionarnoy sistemy, voznikayushey v dvuxskorostnoy gidrodinamike // SibJVM, 2017, t. 20, No. 4, s. 425-437.

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