Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 17.09.1964
E-mail:
Keywords: group analysis, kinetic equations, momentum system, wave equation in nonhomogeneous media, eiconal, differential equation on network, oscillation spectral theorems, Green function of boundary value problem, sign-regularity of discontinuous boundary value problem, summarising of Fourie series in the order of coefficients decreasing, constructive non-standard analysis.

Subject:

Theory of oscillation spectral properties. The analogue of Kellogg oscillation theorem is obtained for integral operators with discontinuous kernels and with integrating by measure is obtained. The effective conditions of sign-regularity (of Kalafaty type) of discontinuous boundary value problems are discovered. Theory of differential equations on networks. For forth order equations on the network the maximum principle is discovered. The system of determinating conditions for Green"s function of the forth order equation is found, the positivity if Green function proved. The method of the reduction of the problem on the network to a problem on an interval developed. Summarising of Fourie series. The formula of the maximal coeffitient in Fourie series and the formula of its number is obtained. Wave propagation in nonhomogeneous media. The formula of propagating waves for one-dimentional media is obtained. The group classification of eiconal equation for non-homogeneous and anisotropic medium fulfilled. Constructive non-standard analysis. The set of hyperreal values allowing the analysis of singularly perturbed equations is made constractively.Group analysis of kinetic equations and the problem of the closure of the momentum system.

Main publications:

1. Borovskikh A. V., Pokornyi Yu. V., “Sistemy Chebysheva–Khaara v teorii razryvnykh yader Kelloga”, Uspekhi matem. nauk, 49:3 (1994), 3–42      
2. Pokornyi Yu.V., Penkin O.M., Borovskikh A.V., Pryadiev V.L., Lazarev K.P., Shabrov S.A., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, 2004
3. Borovskikh A.V., Perov A.I., Lektsii po obyknovennym differentsialnym uravneniyam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2004
4. Borovskikh A.V., “Metod rasprostranyayuschikhsya voln dlya odnomernoi neodnorodnoi sredy”, Trudy seminara im. I.G. Petrovskogo, 2004, № 24, 3–43
5. Borovskikh A.V., “Uravneniya eikonala dlya neodnorodnoi i anizotropnoi sredy”, Uravneniya matematicheskoi fiziki, Sovremennaya matematika i ee prilozheniya, 64, 18–38

Recent publications

Presentations in Math-Net.Ru

Personal pages:

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Organisations:

• Lomonosov Moscow State University, Russian Federation
• Mathematical Science and Education Center, Khetagurov North Ossetian State University
• Lomonosov Moscow State University
• Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
• Voronezh State University