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.
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.
