Geodesic
Steady oscillations in a continuously inhomogeneous medium described by the Ovsyannikov equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 131-140 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using group analysis methods, for the Ovsyannikov equation with maximal symmetry which describes steady oscillations in a continuously inhomogeneous medium we obtain an exact solution to the boundary value problems for some regions (a generalized Poisson formula), which in particular can serve as test solutions for simulating steady oscillations in continuously inhomogeneous media. We find operators acting on the set of solutions in a one-parameter family of these equations.
Mots-clés : Ovsyannikov equation
Keywords: maximal symmetry, steady oscillations in continuously inhomogeneous medium, intertwining operators, generalized Poisson formula. 
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Yu. A. Chirkunov. Steady oscillations in a continuously inhomogeneous medium described by the Ovsyannikov equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 131-140. http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a11/

[1] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[2] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, ch. 2, Nauka, M., 1963

[3] Riss F., Sëkefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR

[4] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, Izd-vo inostr. lit., M., 1957