Asymptotic mathematics: definition of the subject, method of order equations, asymptotic generalization of the Fourier method; aerodynamics: exact solution of boundary problems for the Chaplygin equation, strict asymptotics of the thin shock layer, local method of the aerodynamic calculation, formulation and solution of the scattering problem on a rough surface; synergetics: open methodology, semantic formula of the system triad.
Biography
Graduated from Faculty of Mathematics and Mechanics of Leningrad State University in 1954 (Department of Hydroaeromechanics). Ph.D. Thesis was defended in 1957. D.Sci. Thesis was defended in 1964. A list of my works contains more than 300 titles.
In 1973 I was awarded the State Prize for papers in aerodynamics.
Main publications:
Barantsev R. G. On singularities of the Tricomi problem solution by the Fourier method // Mixed Type Equations. Leipzig: Teubner, 1986, p. 47–54.
Barantsev R. G. Asymptotic versus classical mathematics // Topics in Math. Analysis. Singapore e.a.: World Sci, 1989, p. 49–64.
R. G. Barantsev, “Critical frequencies influence on formulation of the problem of a thin wing oscillation in a gas flow”, Dal'nevost. Mat. Zh., 4:2 (2003), 226–230
R. G. Barantsev, V. V. Grudtsyn, “Asymptotic behavior of the Fourier coefficients for the problem of scattering on contours $r=(1+\beta\cos\varphi)^\gamma$”, Zap. Nauchn. Sem. LOMI, 62 (1976), 27–38; J. Soviet Math., 11:5 (1979), 680–686
R. G. Barantsev, “The method of separation of variables in the problem of scattering by a body of arbitrary shape”, Dokl. Akad. Nauk SSSR, 147:3 (1962), 569–570
R. G. Barantsev, “Expansion theorems connected with boundary problems for equation $u_{xx}-K(x)u_{tt}=0$ within the strip $0\le x\le1$
with degeneration or singularity at the boundary”, Dokl. Akad. Nauk SSSR, 121:1 (1958), 9–12
R. G. Barantsev, “Two expansion theorems connected with boundary problems for the equation $\psi_{\sigma\sigma}-K(\sigma)\psi_{\theta\theta}=0$”, Dokl. Akad. Nauk SSSR, 117:4 (1957), 551–554
R. G. Barantsev, “A mixed problem for equation $\psi_{\sigma\sigma}-K(\sigma)\psi_{\theta\theta}=0$ with Cauchy data given on curve $\theta=s(\sigma)$”, Dokl. Akad. Nauk SSSR, 114:5 (1957), 919–922
15.
R. G. Barantsev, “A boundary problem for equation $\psi_{\sigma\sigma}-K(\sigma)\psi_{\theta\theta}=0$ values given on the characteristic and $\sigma=\operatorname{const}$ lines”, Dokl. Akad. Nauk SSSR, 113:5 (1957), 955–958
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