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8 Gubkina St. Moscow,
119991, Russia
Tel.: +7(495) 984 81 41
Fax: +7(495) 984 81 39
Web site: www.mi-ras.ru
E-mail: steklov@mi-ras.ru

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Department of Mechanics

| Seminars | History of the Department | Research fields | Publications |
Staff
Bolotin Sergei Vladimirovich

Doctor Phys.-Math. Sci., Professor, Corresponding Member of RAS, Head of Department, Chief Scientific Researcher
office: 436; tel.: +7 (495) 984 81 41 * 39 77, +7 (495) 984 81 41 * 35 44; e-mail: bolotin@mi-ras.ru
Principal fields of research: Hamilton systems. Variational methods.
Bolotin Sergei Vladimirovich
Alekseev Georgy Andreevich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 505; tel.: +7 (495) 984 81 41 * 39 50, +7 (495) 984 81 41 * 36 58; e-mail: G.A.Alekseev@mi-ras.ru
Principal fields of research: General relativity and gravitation theory (mathematical methods). Theory of nonlinear integrable systems. Integrable reductions of Einstein's equations (internal structure, solution generating methods, and solution of nonlinear initial and boundary value problems). Investigation of nonlinear properties of gravitational fields and of their interactions with various matter fields via construction of physically interesting field configurations with subsequent analysis of their physical and geometrical properties.
Alekseev Georgy Andreevich
Bogolyubov (Jr.) Nikolai Nikolaevich

Doctor Phys.-Math. Sci., Corresponding Member of RAS, Chief Scientific Researcher
office: 532; tel.: +7 (499) 941 01 73; +7 (495) 984 81 41 * 36 38; e-mail: bogolubv@mi-ras.ru
Chugainova Anna Pavlovna

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 516; tel.: +7 (499) 941 01 75, +7 (495) 984 81 41 * 36 59; e-mail: A.P.Chugainova@mi-ras.ru
Principal fields of research: Shock waves in media. Propagation of waves in elastic and viscoelastic media with dispersion. Nonuniqueness of solutions of automodel problems for nonlinear dynamical elasticity theory.
Chugainova Anna Pavlovna
Dymov Andrej Victorovich

PhD, Senior Scientific Researcher
office: 410; tel.: +7 (495) 984 81 41 * 39 75; e-mail: adymov88@gmail.com
Il'ichev Andrei Teimurazovich

Doctor Phys.-Math. Sci., Professor, Leading Scientific Researcher
office: 504; tel.: +7 (495) 984 81 41 * 37 36, +7 (495) 984 81 41 * 36 54; e-mail: ilichev@mi-ras.ru
Personal page: https://homepage.mi-ras.ru/~ilichev
Principal fields of research: Nonlinear waves. Dispersive and dissipative media. Hamiltonian systems. Orbital stability of bound states. Solitary waves. Exponential instability. Evans function. Collapse. Asymptotic methods. Qualitative theory of dynamical systems. Center manifold reduction. Normal forms.
Il'ichev Andrei Teimurazovich
Kozlov Valerii Vasil'evich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Chief Scientific Researcher
office: 533; tel.: +7 (495) 984 81 41, +7 (495) 984 81 41 * 37 28; e-mail: vvkozlov@mi-ras.ru
Principal fields of research: Analytical mechanics with applications to adjacent areas of theory of dynamical systems. Variational calculus. Differential topology and stability theory.
Kozlov Valerii Vasil'evich
Kulikovskii Andrei Gennad'evich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Chief Scientific Researcher
office: 516; tel.: +7 (499) 941 01 75, +7 (495) 984 81 41 * 36 59; e-mail: kulik@mi-ras.ru
Principal fields of research: Magnetohydrodynamics. Shock waves in continuous media. Asymptotical methods for stability of flows of continuous media in extended regions.
Kulikovskii Andrei Gennad'evich
Markov Vladimir Vasil'evich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 504; tel.: +7 (495) 984 81 41 * 37 36, +7 (495) 984 81 41 * 36 54; e-mail: markov@mi-ras.ru
Principal fields of research: Flows of continuous media with chemical reactions and radiation transport. Movements of rigid and fluid particles and nonstationary gas flows. Propagation of more-than-one dimensional and nonstationary fronts of detonation. Initiation and extinction of detonation.
Markov Vladimir Vasil'evich
Polekhin Ivan Yur'evich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 410; tel.: +7 (495) 984 81 41 * 39 75; e-mail: ivanpolekhin@gmail.com
Personal page: https://homepage.mi-ras.ru/~ivanpolekhin
Soldatov Andrei Vladimirovich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 531, 305; tel.: +7 (495) 984 81 41 * 35 86, +7 (499) 941-03-63; e-mail: soldatov@mi-ras.ru
Soldatov Andrei Vladimirovich
Treschev Dmitrii Valer'evich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Director
office: 326; tel.: +7 (495) 984 81 41; e-mail: treschev@mi-ras.ru
Personal page: https://homepage.mi-ras.ru/~treschev
Principal fields of research: Dynamical systems of classic mechanics.
Treschev Dmitrii Valer'evich
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Seminars
Dynamical Systems and Mathematical Physics
Seminar organizer: A. V. Dymov; D. V. Treschev
Steklov Mathematical Institute, Gubkina 8, room 313
Dynamical Systems and PDEs
Paris 7 Diderot & Steklov Mathematical Institute Online Seminar
Hamiltonian systems and statistical mechanics
MSU, auditorium 14-02
Seminar of the Department of Mechanics
Steklov Mathematical Institute, Room 530 (8 Gubkina)
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History of the Department

After the foundation of Steklov Mathematical Institute in 1934, two departments of mechanics were organized: Department of Elasticity Theory headed by N. I. Muskhelishvili and Department of Continuous Media headed by N. E. Kochin. These departments were closed after the departure of N. I. Muskhelishvili to Georgia and N. E. Kochin's transition to a newly founded Institute of Mechanics of the Academy of Sciences.

Department of Mechanics at the Mathematical Institute was organized again in 1944 (headed by M. V. Keldysh). After M. V. Keldysh moved in 1953 to a newly founded Institute of Applied Mathematics, L. I. Sedov was appointed as the head of the department and he held this appointment till 1988. From 1988 to 2003 the department was headed by A. G. Kulikovskii, and from 2003 to 2011 by V. V. Kozlov. Art present the duties of the head of the department are fulfilled by S. V. Bolotin.

In 2002, the Department of Mechanics united with the Department of Statistical Mechanics which was established in 1969 under the leadership of N. N. Bogolubov (Jr). At present the staff of the Department includes members of RAS V. V. Kozlov and A. G. Kulikovskii, correspondent members of RAS N. N. Bogolubov and D. V. Treschev; doctors of phys.-math. sci. G. A. Alekseev, S. V. Bolotin, A. P. Chugainova, A. T. Il'ichev, V. V. Markov, D. P. Sankovich, candidate of phys.-math. sci. A. V. Soldatov.

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Research fields

  • analytical methods and numerical simulation of nonlinear fenomena in various problems of mechanics of continuous media, stability of flows, propagation of wave fronts and shock waves of various structures in inhomogeneous and anisotropic media with dissipative and dispersive properties, interactions of nonlinear waves and shock waves (A. G. Kulikovskii and A. P. Chugainova);
  • investigation with analytical and numerical methods of waves propagation in dispersive media, stability of localized wave structures and interfaces in various problems of hydromechanics, elasticity theory and theory of filtration (A. T. Il'ichev);
  • numerical simulation of flows of continuous media with chemical reactions, radiation transport, movements of rigid and fluid particles in gas flows, propagation of nonstationary detonation fronts, initiation and extinction of detonation (V. V. Markov);
  • theory of integrable space-time symmetry reductions of Einstein's, Einstein–Maxwell and other field equations of the gravitation theory and investigation of nonlinear properties of strong gravitational fields (G. A. Alekseev);
  • mathematical methods of investigation of physical systems interacting with bosonic fields, including polaron-type systems and quantum low-dimensional systems (N. N. Bogolubov (Jr.), A. V. Soldatov);
  • mathematically rigorous approach to the investigation of the thermodynamically equilibrium properties of strongly non-ideal Bose- and Fermi-systems on the basis of the correlation inequalities formalism; determination of the conditions under which various phase transitions can take place; rigorous proof of the Bose-condensation in the mentioned above quantum systems (D. P. Sankovich);
  • nonequilibrium methods of statistical mechanics, including the method of the self-consistent projection operator and methods based on the exact evolution equations formalism, with the purpose of the electromagnetic field-matter interaction investigation with possible applications to problems of quantum optics;
  • investigations of the irreversible evolution of quantum atomic systems interacting with the electromagnetic field with the purpose to obtain rigorous results regarding the nonequilibrium behavior (relaxation, decay) of such systems;
  • mathematical methods of nonequilibrium statistical mechanics with applications to the problem of interaction of model atomic systems with external polychromatic electromagnetic fields; investigation of the spectroscopic properties of the composite quantum systems resulting from this interaction (N. N. Bogolubov (Jr.) and A. V. Soldatov);
  • variational methods of classical mechanics (S. V. Bolotin, V. V. Kozlov);
  • periodic and chaotic solutions of the 3 body problem (S. V. Bolotin);
  • problem of integrability of the equations of motion (V. V. Kozlov, D. V. Treschev);
  • nonholonomic mechanical systems and rolling of rigid bodies (V. V. Kozlov, D. V. Treschev);
  • mathematical problems of statistical mechanics (V. V. Kozlov, D. V. Treschev);
  • KAM theory and the problem of Arnold's diffusion (D. V. Treschev).

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