01.01.02 (Differential equations, dynamical systems, and optimal control)
differential equations and applications,
mathematical models and partial differential equations,
lattice of connected oscillators,
For singularly perturbed systems of ordinary differential equations the general asymptotic theory of periodic solutions close to discontinuous solutions (modeling relaxation oscillations) is constructed; the trajectories-duck etc. problems were studied. For singularly perturbed partial differential equations the periodic motions and bifurcation processes were investigated; the theoretical justification of a new buffer phenomenon (which could be watched in many mathematical models of natural sciences and technique, which described by the hyperbolic and parabolic type equations) is gave. The investigations were realized in cooperation with E. F. Mishchenko and A. Yu. Kolesov. The results in the general and qualitative theory of the ordinary differential equations (distribution of the Lyapuniv exponents etc.), in theory of controllable systems (stabilization of non-stable non-stationary systems etc.), in theory of optimal control and differential games (investigation of an alternating Pontriagin integral etc.) are obtained, in theory of partial differential equations (the asymptotical solution of singularly perturbed equations of mixed type etc.), in applications of the differential equations (for example, to a theory of oscillations). The series of the publications is dedicated to the content and procedure of teaching of mathematics in secondary and high schools, architecture of mathematical education, history and methodology of mathematics, propaganda of mathematical knowledge among youth.
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1958 (Department of differential equations). Ph.D. thesis was defended in 1964 (scientific chief E. F. Mishchenko). D.Sci. thesis was defended in 1983. Since 1961 I was an assistant professor of the Department of differential equations of Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU), since 1966 — an associate professor of this Department, since 1989 I am a professor of the same Department. A list of my works contains more than 150 scientific papers, 13 monographs and textbooks. I has prepared 19 candidates of sciences (5 of them became the doctors of sciences). Since 1978 V. A. Kondratiev, V. M. Millionshchikov and I have led the research seminar at MSU on qualitative theory of the differential equations. Since 2000 I have led the research seminar at MSU on methodology of usage of modern informational technology and electronic devices in educational process.
In 1966–1970 I was a vice dean of the Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University In 1968–1987 I was a head of the division "Ordinary differential equations" of the Referativny journal "Mathematics" (Moscow), senior scientific researcher of Russian Institute for Scientific and Technical Information. Since 1997 I am a dean-organizer of the Faculty of Pedagogical Education of M. V. Lomonosov Moscow State University and the head of the Department of educational technologies of this faculty. I am the member of editorial boards of issues: Referativny journal "Mathematics", "Proceedings of the Moscow mathematical society", "Proceedings of I. G. Petrowsky seminar", "Differential equations", "Memoirs on Differential Equations and Mathematical Physics" (Georgia), "Nonlinear Oscillations" (Ukraine), "Quantum", "Mathematical enlighten". I am the editor-in-chief of a journal "Bulletin of the Moscow State University. Series "Pedagogical education". I am the member of Presidiums of Scientific-methodical council on mathematics and Council on pedagogical education of Ministry of education of Russian Federation, Commission of Russian academy of sciences on school mathematical education. I am the member of an International Higher Education Academy of Sciences, International Academy of Informatization, Academy of Nonlinear Sciences; the foreign member of a National Academy of Sciences of Madagascar.
Mishchenko E. F., Rozov N. Kh. Differential equations with small parameters and relaxation oscillations. New York: Plenum Press, 1980. 230 pp.
Mishchenko E. F., Kolesov Yu. S., Kolesov A. Yu., Rozov N. Kh. Asymptotic methods in singularly perturbed systems. New York: Consult. Bureau, Plenum Publ. Corp., 1994. 281 pp.
Kolesov A. Ju., Mishchenko E. F., Rozov N. Kh. Asymptotic methods of invistigation of periodic solutions of nonlinear hyperbolic equations // Proc. Steklov Inst. of Math. 1998. V. 222. P. 3–188.
Dorofeev G., Potapov M., Rozov N. Elementary mathematics. M.: Mir., 1988. 490 pp.
In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014) I. V. Gaishun, A. A. Gryzlov, V. Ya. Derr, N. A. Izobov, A. I. Karpov, E. K. Makarov, G. V. Merzlyakova, N. N. Petrov, S. N. Popova, L. I. Rodina, N. Kh. Rozov, I. N. Sergeev, A. A. Tolstonogov, V. N. Ushakov, A. G. Chentsov Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4, 146–154
Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010 M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova CMFD, 39 (2011), 5–10
Olga Arsenjevna Oleinik I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. Yu. Goritskii, N. V. Denisova, V. V. Zhikov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova Tr. Semim. im. I. G. Petrovskogo, 28 (2011), 5–7
Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday) A. V. Arutyunov, Yu. N. Bibikov, F. P. Vasil'ev, I. V. Gaishun, S. V. Emel'yanov, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, S. A. Mazanik, E. K. Makarov, A. A. Martynyuk, E. F. Mishchenko, E. I. Moiseev, Yu. S. Osipov, V. A. Pliss, N. Kh. Rozov, V. A. Sadovnichy, A. M. Samoilenko, T. K. Shemjakina Differ. Uravn., 46:1 (2010), 3–8
In memory of Evgenii Frolovich Mishchenko Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov Tr. Mat. Inst. Steklova, 271 (2010), 7–8
Vladimir Alexandrovich Kondratiev on the 70th anniversary of his birth 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 Tr. Semim. im. I. G. Petrovskogo, 26 (2007), 5–28
Ol'ga Arsen'evna Oleinik (obituary) T. D. Venttsel', V. S. Vladimirov, V. V. Zhikov, A. M. Il'in, V. A. Il'in, V. A. Kondrat'ev, L. D. Kudryavtsev, E. F. Mishchenko, S. M. Nikol'skii, Yu. S. Osipov, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, L. D. Faddeev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov Uspekhi Mat. Nauk, 58:1(349) (2003), 165–174
Anatolii Sergeevich Kalashnikov (obituary) T. D. Venttsel', Yu. A. Dubinskii, A. M. Il'in, V. A. Kondrat'ev, V. P. Mikhailov, A. A. Mal'tsev, O. A. Oleinik, S. I. Pokhozhaev, N. Kh. Rozov, G. A. Chechkin, T. A. Shaposhnikova Uspekhi Mat. Nauk, 55:5(335) (2000), 161–168