A continuous approximation for a~1D analogue of the Gol'dshtik model for separated flows of incompressible fluid
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 291-296.

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A modification of a 1D analogue of the Gol'dshtik mathematical model for separated flows of incompressible fluid is considered. The model is a nonlinear differential equation with a boundary condition. Nonlinearity in the equation is continuous and depends on a small parameter. When this parameter tends to zero, we have a discontinuous nonlinearity. The results of the solutions are in accord with the results obtained for the 1D analogue of the Gol'dshtik model for separated flows of incompressible fluid.
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D. K. Potapov. A continuous approximation for a~1D analogue of the Gol'dshtik model for separated flows of incompressible fluid. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 291-296. http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a4/

[1] Goldshtik M. A., “Matematicheskaya model otryvnykh techenii neszhimaemoi zhidkosti”, Dokl. AN SSSR, 147:6 (1962), 1310–1313

[2] Potapov D. K., “Matematicheskaya model otryvnykh techenii neszhimaemoi zhidkosti”, Izvestiya RAEN. Ser. MMMIU, 8:3–4 (2004), 163–170

[3] Potapov D. K., “Nepreryvnye approksimatsii zadachi Goldshtika”, Matem. zametki, 87:2 (2010), 262–266 | MR | Zbl

[4] Krasnoselskii M. A., Pokrovskii A. V., “Uravneniya s razryvnymi nelineinostyami”, Dokl. AN SSSR, 248:5 (1979), 1056–1059 | MR

[5] Potapov D. K., “Ustoichivost osnovnykh kraevykh zadach ellipticheskogo tipa so spektralnym parametrom i razryvnoi nelineinostyu v koertsitivnom sluchae”, Izvestiya RAEN. Ser. MMMIU, 9:1–2 (2005), 159–165

[6] Pavlenko V. N., Potapov D. K., “Approksimatsiya kraevykh zadach ellipticheskogo tipa so spektralnym parametrom i razryvnoi nelineinostyu”, Izvestiya vuzov. Matematika, 2005, no. 4, 49–55 | MR | Zbl

[7] Potapov D. K., “Approksimatsiya zadachi Dirikhle dlya uravneniya ellipticheskogo tipa vysokogo poryadka so spektralnym parametrom i razryvnoi nelineinostyu”, Diff. uravneniya, 43:7 (2007), 1002–1003 | MR | Zbl

[8] Pavlenko V. N., Potapov D. K., “O suschestvovanii lucha sobstvennykh znachenii dlya uravnenii s razryvnymi operatorami”, Sib. mat. zhurn., 42:4 (2001), 911–919 | MR | Zbl

[9] Potapov D. K., “Ob odnoi otsenke sverkhu velichiny bifurkatsionnogo parametra v zadachakh na sobstvennye znacheniya dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami”, Diff. uravneniya, 44:5 (2008), 715–716 | MR | Zbl

[10] Krasnoselskii M. A., Pokrovskii A. V., “Pravilnye resheniya uravnenii s razryvnymi nelineinostyami”, Dokl. AN SSSR, 226:3 (1976), 506–509 | MR