Alexander I. Komech, Senior Scientist

Director of Research in French-Russian A.M.Liapunov Institute of Moscow State University.

Date of birth: May, 5, 1946.
Degree: PhD (Candidate of Scienses)1974, Moscow State University
fax: (7-095) 932-89-52

Subjects of researches:

Stabilization of statistical solutions to wave and Klein-Gordon equations. Statistical solutions to Navier-Stokes system. Large deviations of solutions to stochastic non-linear parabolic partial differential equations. Long-time asymptotics and attractors of solutions to nonlinear hyperbolic partial differential equations. Boundary value problems in the regions with corners. Diffraction of waves on a wedge. Mathematical problems of quantum physics and of statistical physics.

Publications: 68 Mathematical papers

Chapters in Books:

  1. ( with M.I.Vishik) "Homogeneous in $x$ Solutions of the Stochastic Navier-Stokes System with White Noise", p.335-556 in the monograph: M.I.Vishik, A.V.Fursikov, "Mathematical Problems in Statistical Hydromechanics", Kluwer Academic Publishers, 1988.
  2. " Linear Partial Differential Equations with Constant Coefficients", p.127-260 in: Encyclopaedia of Mathematical Sciences, v.31, Springer, Berlin, 1994.
  3. Manual-Problems Collection "Practice in Mathematical Physics Equations", Moscow University Publishing, 1986, 159p; 2nd edition 1994.

    Basic publications

    [1] Elliptic boundary value problems on manifolds with piecewise smooth boundary, Math. USSR sbornik, v.21, (1973), no.1, 91-135.
    [2] with A.V.Fursikov, M.I.Vishik, Some mathematical problems of statistical hydromechanics , Russian Math. Surveys v.34, 1979, 149-224.
    [3] ", An estimate for the mean square of the difference of velocities for homogeneous statistical solutions of the three-dimensional Navier-Stokes system, Journal of Soviet Mathematics, v.45, N.5, June, 1989, 1367-1373.
    [4] with V.M.Imajkin, On the large deviations of solutions of non-linear stochastic equations, Trudy sem. I.G.Petrovsky, v.13, 1988, 177-196 (in Russian).
    [5] with Ya.Sh.Il'yasov, Girsanov's theorem and Ergodic Properties of Statistical Solutions of Nonlinear Parabolic Equations , Journal of Soviet Math., v.47, N.3, 1989, 2547-2569.
    [6] with N.E.Ratanov, Stabilization of space-time stochastic Solutions of a Wave Equation , Steklov seminar 1985-1986, v.2, Statistics and Control of Stochastic Processes, Trans. Optimization Soft-Ware, New York, 1989,171-187.
    [7] with E.A.Kopylova and N.E.Ratanov, The stabilization of statistics in wave equations with mixing, p.9-10 in: Tagungsbericht 51/1992, Large Deviations and Applications, 29.11. bis 5.12.1992, Mathematishes Forschungsinstitut Oberwolfach, 1992.
    [8] with E.A.Kopylova and N.E.Ratanov, The stabilization of statistics in wave and Klein-Gordon equations. The scattering theory for the solutions of infinite energy, p.273-274 in: Extended Abstracts. Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, June 7-10, 1993, University of Delaware, p.273-274.
    [9] with V.M.Imajkin, On large deviations and transitivity of solutions to nonlinear stochastic partial differential equations, Russian Journal of Mathematical Physics, 1994, v.2, N.1, 69-92. [10] with A.E.Merzon, General boundary value problems in regions with corners, p.171-183 in: Operator Theory: Advances and Applications, v.57, 1992, Birkhauser Verlag, Basel.
    [11] Stabilization of the interaction of a string with a nonlinear oscillator, Moscow Univ. Math. Bull., v.46, 1991, 34-39. [12] On stabilization of string-nonlinear oscillator interaction, J. Math. Anal. Appl., v.196, 1995, 384-409.
    [13] On the stabilization of string-oscillators interaction, Russian Journal of Mathematical Physics, v.3, 1995, 227-248. [14] Asymptotics of solutions to nonlinear wave equations, p. 22-46. in ''Proceedings of the Third International Conference on Mathematical and Numerical Aspects of Wave Propagation'', 1995, SIAM--INRIA, edited by Gary Cohen.
    [15] On transitions to stationary states in some infinite dimensional Hamiltonian systems, Doklady Mathematics, v.53, 1996, no.2, 208-210. [16] Stabilization of statistics in wave and Klein-Gordon equations with mixing. Scattering theory for infinite energy solutions, Rend. Sem. Mat. Fis. di Milano, v.65, 1995, 9-22.
    [17] with B.R.Vainberg, On asymptotic stability of stationary solutions to nonlinear wave and Klein-Gordon equations, Arch. Rat. Mech. Anal., v.134, 1996, 227-248. [18] with A.E.Merzon and P.Zhevandrov, On Ursell's problem, Russian J. Math. Phys., v.4, 1996, no.4, 55-85.
    [19] On long-time asymptotics and attractors for nonlinear wave equations. Preprint CEREMATH-UT1, 1996, no.3, 1--30.
    [20] On long-time asymptotics and attractors for nonlinear wave equations, in Proceedings of the Conference on Applied Mathematics and Computer Science, Moscow, French-Russian A.M.Liapunov Institute on Applied Mathematics and Computer Science, 1996, 40--64.
    [21] with T.D.Dudnikova, On ergodic properties of hyperbolic equations with mixing, Theory of Probability and Appl., v.41, 1996, no.3, 436-448.
    [22] with T.D.Dudnikova, On stabilization for a nonlinear wave equation, Russ. Math. Surv., v.51, 1996, no.5, 983.
    [23] with H.Spohn and M.Kunze, Long-time asymptotics for a classical particle interacting with a scalar wave field, Comm. Partial Diff. Equs., v.22, 1997, no.1/2, 307-335.
    [24] with H.Spohn, Soliton-like asymptotics for a classical particle interacting with a scalar wave field, accepted in Nonlinear Analysis.
    [25] with J.Fleckinger, On soliton-like asymptotics for 1D nonlinear reaction systems, Russian Journal of Mathematical Physics, v.5, no.3, 1997, 295-307.
    [26] with P.Joly and O.Vacus, On Transitions to Stationary States in a Maxwell-Landau-Lifchitz-Gilbert System, Rapport de Recherche No.3287, INRIA, 1997, 1-32.

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