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.
Biography
Graduated from Voronezh State University (Mathematical Department) in 1986. Candidate (Ph.D.) thesis "Boundary value problems with singularities" — 1990. About 20 referred publications.
Since 1996 — sci. secr. of Voronezh Spring Mathematical Schools and of Voronezh Winter Schools on the Function Theory.
Main publications:
Borovskikh A. V., Pokornyi Yu. V., “Sistemy Chebysheva–Khaara v teorii razryvnykh yader Kelloga”, Uspekhi matem. nauk, 49:3 (1994), 3–42
Borovskikh A.V., “Uravneniya eikonala dlya neodnorodnoi
i anizotropnoi sredy”, Uravneniya matematicheskoi fiziki, Sovremennaya matematika i ee prilozheniya, 64, 18–38
A. V. Borovskikh, “Geometry of the Lie group: Riemann and Ricci tensors and normal forms of Lie algebras”, TMF (to appear)
2023
2.
A. V. Borovskikh, “Lie group geometry. Invariant metrics and dynamical systems, dual algebra, and their applications in the group analysis of a one-dimensional kinetic equation”, Theoret. and Math. Phys., 217:1 (2023), 1528–1540
3.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Goritsky, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, A. A. Kon'kov, V. V. Palin, E. V. Radkevich, V. V. Rogachev, O. S. Rozanova, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, M. V. Shamolin, T. A. Shaposhnikova, Tr. Semim. im. I. G. Petrovskogo, 33, 2023, 3–7
2021
4.
K. S. Platonova, A. V. Borovskikh, “Group analysis of the one-dimensional Boltzmann
equation. Invariants and the problem of moment system closure”, Theoret. and Math. Phys., 208:3 (2021), 1165–1181
2020
5.
K. S. Platonova, A. V. Borovskikh, “Group analysis of the Boltzmann and Vlasov equations”, Theoret. and Math. Phys., 203:3 (2020), 794–823
6.
I. V. Astashova, A. V. Borovskikh, G. Yu. Riznichenko, “In memory of Rozov Nikolai Khristovich”, Computer Research and Modeling, 12:6 (2020), 1265–1267
2019
7.
A. V. Borovskikh, K. S. Platonova, “Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general case”, Theoret. and Math. Phys., 201:2 (2019), 1612–1642
2018
8.
K. S. Platonova, A. V. Borovskikh, “Group analysis of the one-dimensional Boltzmann equation: III. Condition for the moment quantities to be physically meaningful”, Theoret. and Math. Phys., 195:3 (2018), 886–915
2015
9.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, N. A. Izobov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. V. Palin, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, E. V. Radkevich, O. S. Rozanova, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Scientific heritage of Vladimir Mikhailovich Millionshchikov”, J. Math. Sci. (N. Y.), 210:2 (2015), 115–134
2014
10.
A. V. Borovskikh, “Eikonal equation for anisotropic media”, J. Math. Sci. (N. Y.), 197:2 (2014), 248–289
Borovskikh A.V., Rozov N.Kh., “Metod sotsializatsii kak sposob preodoleniya proizvolnosti uslovii v igre i obuchenii”, Igra kak uslovie i mekhanizm razvitiya. Mater. 2-oi Ezhegodn. konf. po igram v obrazovanii., Krasnogorsk Moskovskoi obl., 3-5 dekabrya 2010 g., Krasnogorskii filial RANKhiGS pri Prezidente RF, Krasnogorsk Moskovskoi obl., 2010, 277-285
38.
Borovskikh A.V., Rozov N.Kh., “O bednom protsente zamolvite slovo...”, Matematika v shkole, 2010, no. 3, 3-15
39.
Borovskikh A.V., Rozov N.Kh., “Nekotorye mysli o pedagogicheskikh realiyakh”, Vestnik Uralskogo instituta ekonomiki, upravleniya i prava., 2010, no. 4, 92-97
40.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, V. V. Kozlov, V. A. Kondratiev, A. A. Kon'kov, N. Kh. Rozov, I. N. Sergeev, V. N. Chubarikov, A. T. Fomenko, A. S. Shamaev, “To memory of Vladimir Mikhailovich Millionshchikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 2, 71–72
Borovskikh A.V., “Group analysis of eikonal equation for non-homogeneous and anisotropic medium”, Abstr. of Intern. Conf. “Symmetry in non-linear physics” (Kiev, 21-27 iyunya 2009 g.), IM NAN Ukrainy, Kiev, 2009, po ssylke http://imath.kiev.ua/~appmath/
Borovskikh A.V., Rozov N.Kh., Shamaev A.S., “Pervyi opyt organizatsii pedagogicheskoi sektsii na konferentsii, posvyaschennoi pamyati I.G.Petrovskogo”, Matematika v vysshem obrazovanii, 2008, no. 8, 9-10
49.
Borovskikh A.V., Perov A.I., “O nekotorykh metodicheskikh printsipakh uchebnika po obyknovennym differentsialnym uravneniyam”, Matematika v vysshem obrazovanii, 2008, no. 6, 45-49
50.
Rozov N.Kh., Reikhani E., Borovskikh A.V., V'zlite v uchilische. Urotsi za razvivane na prostranstvenogo mislene, Fondatsiya “Mlada B'lgariya”, Sofiya, 2008 , 162 pp., (na bolgarskom yazyke)
2007
51.
Borovskikh A.V., “Formulas of boundary control of an inhomogeneous string: I”, Differential Equations, 43:1 (2007), 69-95
52.
Borovskikh A.V., “Formulas of boundary control of an inhomogeneous string: II”, Differential Equations, 43:5 (2007), 656-666
53.
Borovskikh A.V., Rozov N.Kh., “O materialnoi i simvolnoi kulture v shkolnom obrazovanii”, Teoriya i praktika innovatsionnoi deyatelnosti v obrazovanii, MAKS Press, Moskva, 2007, 14-17
54.
Borovskikh A.V., Reikhani E., Rozov N.Kh., “Razvitie geometricheskogo myshleniya shkolnikov”, Teoriya i praktika innovatsionnoi deyatelnosti v obrazovanii, MAKS Press, Moskva, 2007, 28-46
55.
Borovskikh A.V., Reikhani E., Rozov N.Kh., “Uzly v shkole”, Teoriya i praktika innovatsionnoi deyatelnosti v obrazovanii, MAKS Press, Moskva, 2007, 47-62
Rozov N.Kh, Reihani E., Borovskikh A.V., Knots at school. Lessons of the development of the spatial thinking, KDU, Moscow, 2007
59.
I. V. Astashova, L. A. Bagirov, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev on the 70th anniversary of his birth”, J. Math. Sci. (N. Y.), 143:4 (2007), 3183–3197
2006
60.
A. V. Borovskikh, “The two-dimensional eikonal equation”, Siberian Math. J., 47:5 (2006), 813–834
61.
Borovskikh A.V., “Equivalence groups of eikonal equation and classes of equivalent equations”, Bulletin of NSU, 2006, no. 4, 3-42
62.
Borovskikh A.V., Rasprostranenie voln v neodnorodnoi srede, Diss.…doktora fiz.-mat. nauk. 01.01.02 – Differentsialnye uravneniya., MGU, Moskva, 2006 , 300 pp.
63.
A. V. Borovskikh, “Equivalence groupes of eikonal equation and classes of equivalent equations”, Vestnik, Quart. J. of Novosibirsk State Univ., Series: Math., mech. and informatics, 6:4 (2006), 3–42
2005
64.
Borovskikh A.V., “An expression of the Riemann function of the wave equation in an Inhomogeneous medium via the transport coefficients”, Differential equations, 41:6 (2005), 895-896
65.
Borovskikh A.V., “Group analysis of the two-dimentional eikonal equation”, Differential equations, 41:6 (2005), 899
Borovskikh A.V., “Rasprostranenie voln v neodnorodnoi srede”, Sovremennye problemy teorii funktsii i ikh prilozheniya: Tez. dokl. 12-i Saratovskoi zimnei shkoly. (Saratov, 27 yanvarya – 3 fevralya 2004 g.), SGU, Saratov, 2004, 32-33
71.
Borovskikh A.V., “Investigation of Relaxation Oscillations with the Use of Constructive Nonstandard Analysis: I.”, Differential Equations, 40:3 (2004), 309-317
72.
Borovskikh A.V., “Investigation of Relaxation Oscillations with the Use of Constructive Nonstandard Analysis: II”, Differential Equations, 40:4 (2004), 491-501
Borovskikh A.V., “Uravnenie eikonala v neodnorodnoi srede”, Tez. dokl. Mezhdunar. konf. po differentsialnym uravneniyam i dinamicheskim sistemam (Suzdal, 5-10 iyulya 2004 g.), VGPU, Vladimir, 2004, 39-40
2005
77.
Borovskikh A.V., “Method of Propagating Waves for a One-Dimensional Inhomogeneous Medium”, Journal of Mathematical Sciences, 127:5 (2005), 2135-2158
2004
78.
Borovskikh A.V., “The Moving Source Phantom in Geometric Optics of Inhomogeneous Media”, Differential Equations, 40:7 (2004), 927-933
79.
Borovskikh A.V., “On a certain Luzin problem”, Analysis. Mathematica, 30:4 (2004), 259-287
80.
Borovskikh A.V., Perov A.I., Lectures on ordinary differential equations, 1, RC “Regular and chaotic dynamics” Institute of Computer Research, Moscow-Izhevsk, 2004 , 540 pp.
81.
Borovskikh A.V., Il'in V.A., Pokornyi Yu.V., ““Pontryagin Readings – XV” at Voronezh Mathematical School “Modern methods in Qualitative Theory of Boundary Value Problems””, Differential Equations, 40:11 (2004), 1665-1666
2003
82.
A. V. Borovskikh, “Sign Regularity Conditions for Discontinuous Boundary-Value Problems”, Math. Notes, 74:5 (2003), 607–618
83.
Pokornyi Y.V., Pryadiev V.L., Borovskikh A.V., “The wave equation on a spatial network”, Doklady Mathematics, 67:1 (2003), 10-12
Borovskikh A.V., “Illusion of the moving source in geometric optics of non-homogeneous medium”, International Seminar “Days on Diffraction”. Abstracts. (S.-Peterburg, 24-27 iyunya 2003 g.), S.-Pb otdelenie MIRAN, S.-Peterburg, 2003, 17
87.
Borovskikh A.V., “The eiconal equation in an inhomogeneous medium”, Doklady Mathematics, 68:1 (2003), 103-106
2005
88.
Borovskikh A.V., “Group Classification of Eikonal Equations for the Wave Equation in Inhomogeneous Media”, Journal of Mathematical Sciences, 129:1 (2005), 3537-3549
2003
89.
P. L. Ul'yanov, Yu. V. Pokornyi, A. V. Borovskikh, “Contemporary methods in theory of functions and adjacent problems”, Uspekhi Mat. Nauk, 58:4(352) (2003), 177–178
90.
Il'in V.A., Pokornyi Yu.V., Borovskikh A.V., ““Pontryagin Readings – XIV” at Voronezh Mathematical School “Modern methods in Qualitative Theory of Boundary Value Problems””, Differential Equations, 39:11 (2003), 1661-1662
91.
V. A. Il'in, Yu. V. Pokorny, A. V. Borovskikh, Differ. Uravn., 39:11 (2003), 1574
2002
92.
Borovskikh A.V., “Summirovanie primera Feiera v poryadke ubyvaniya koeffitsientov”, Tez. dokl. shkoly “Sovremennye problemy teorii funktsii i ikh prilozheniya” (Saratov, 27 yanvarya – 3 fevralya 2002 g.), Saratovskii gosuniversitet, Saratov, 2002, 36
93.
Borovskikh A.V., Lazarev K.P., “Printsip maksimuma dlya differentsialnykh uravnenii chetvertogo poryadka na grafakh”, Tez. dokl. shkoly “Sovremennye problemy teorii funktsii i ikh prilozheniya” (Saratov, 27 yanvarya – 3 fevralya 2002 g.), Saratovskii gosuniversitet, Saratov, 2002, 37
Borovskikh A.V., Gruppovaya klassifikatsiya uravnenii eikonala dlya volnovogo uravneniya v neodnorodnoi srede, Dep. v VINITI 29.05.2002, N 953-V2002., VINITI, Moskva, 2002 , 143 pp.
98.
Borovskikh A.V., “A Traveling Wave Formula in a One-Dimensional Inhomogeneous Medium”, Differential Equations, 38:6 (2002), 796-807
99.
Borovskikh A.V., “Group classification of eikonal equation for an inhomogeneous medium”, Differential Equations, 38:11 (2002), 1669-1670
100.
Borovskikh A.V., “Geomerty of fronts and rays in a medium with linear and quadratic velocity function”, Differential Equations, 38:11 (2002), 1673
101.
Borovskikh A.V., “Application of constructive non-standard analysis to investigation of a system of connected Van-der-Pol equations”, Differential Equations, 38:11 (2002), 1678-1679
102.
Pokornyi Yu.V., Borovskikh A.V., “On defects of axiomatics of Green's function”, Doklady Mathematics, 65:3 (2002), 399-403
Pokornyi Yu.V., Borovskikh A.V., “Differential equations on networks (geometrical graphs)”, Journal of Mathematical Sciences, 119:6 (2004), 691-718
105.
Borovskikh A.V., Lazarev K.P., “Differential equations of the forth order on geometrical graphs”, Journal of Mathematical Sciences, 119:6 (2004), 719-738
106.
Pokornyi Yu.V., Borovskikh A.V., “Connection between the Green's function and the influence function for the non-classical problems”, Journal of Mathematical Sciences, 119:6 (2004), 739-768
2001
107.
Borovskikh A.V., “Rasprostranenie voln v odnomernoi neodnorodnoi srede”, Tez. dokl. shkoly “Sovremennye metody teorii funktsii i smezhnye problemy” (Voronezh, 27 yanvarya – 4 fevralya 2001 g.), VGU, Voronezh, 2001, 50-51
108.
Borovskikh A.V., “Konstruktivnyi nestandartnyi analiz”, Analiticheskie i chislennye metody v matematike i mekhanike. Tr. XXII konf. molodykh uchenykh mekh.-mat. f-ta MGU. (Moskva, 17-22 aprelya 2000 g.), izd-voMGU, Moskva, 2001, 28-31
109.
Borovskikh A.V., “Volny v odnomernoi neodnorodnoi srede”, Sovremennye metody v teorii kraevykh zadach. “Pontryaginskie chteniya - XII”. Tez. dokl. shkoly. (Voronezh, 3-9 maya 2001 g.), VGU, Voronezh, 2001, 34-35
Yu. V. Pokornyi, P. L. Ul'yanov, A. V. Borovskikh, “Voronezh Winter Mathematical School “Modern Methods in Theory of Functions and Adjacent Problems””, Uspekhi Mat. Nauk, 56:4(340) (2001), 185–186
Borovskikh A.V., Analiz beskonechno malykh velichin. Ch. I. Arifmetika, algebra, funktsii, printsip formalnoi invariantnosti, Dep. v VINITI. 13.12.00, N 3133-V00., VINITI, Moskva, 2000 , 87 pp.
118.
Borovskikh A.V., Rasprostranenie voln v odnomernoi neodnorodnoi srede, Dep. v VINITI 13.12.00, N 3134-V00., VINITI, Moskva, 2000 , 52 pp.
119.
P. L. Ul'yanov, Yu. V. Pokornyi, A. V. Borovskikh, ““Modern Methods in Theory of Functions and Adjacent Problems” on Voronezh Winter Mathematical School”, Uspekhi Mat. Nauk, 55:2(332) (2000), 189–190
A. V. Borovskikh, K. P. Lazarev, Yu. V. Pokornyi, “On the Kellogg kernels in discontinuous problems”, Proc. Steklov Inst. Math., 211 (1995), 92–108
135.
Borovskikh A.V., “Ob ekstremumakh razryvnykh sistem Chebysheva i Markova”, Tez. dokl. shkoly “Sovremennye metody teorii funktsii i smezhnye problemy prikladnoi matematiki i mekhaniki” (Voronezh, 25 yanvarya – 1 fevralya 1995 g.), VGU, Voronezh, 1995, 48
136.
Borovskikh A.V., Kolmykov V.A., “Integrirovanie po diskretnym meram na grafakh”, Tez. dokl. shkoly “Sovremennye metody teorii funktsii i smezhnye problemy prikladnoi matematiki i mekhaniki” (Voronezh, 25 yanvarya – 1 fevralya 1995 g.), VGU, Voronezh, 1995, 49
Borovskikh A.V., Burlutskaya M.Sh., “O differentsirovanii i integrirovanii po mere na abstraktnykh lineinykh kontinuumakh i o kvazichislakh”, Tez.dokl. II mezhdun. konferentsii “Algebraicheskie, veroyatnostnye, geometricheskie, kombinatornye i funktsionalnye metody v teorii chisel” (Voronezh, 25-30 sentyabrya 1995 g.), VGU, Voronezh, 1995, 25
143.
Borovskikh A.V., Mustafokulov R., Lazarev K.P., Pokornyi Yu.V., “A class of fourth-order differential equations on a spatial net”, Doklady Mathematics, 52:3 (1995), 433-435
Borovskikh A.V., Pryadiev V.L., Analog zadachi Emdena dlya singulyarnogo sluchaya, Voronezh. un-t. Voronezh / Dep. v VINITI 25.12.85, # 8801-V, VINITI, Moskva, 1985 , 11 pp.
Presentations in Math-Net.Ru
1.
Содержание математического образования: математика для не-математиков A. V. Borovskikh VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 16, 2023 16:30
2023
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