Bratus', Alexander Sergeevich

Statistics Math-Net.Ru
Total publications: 19
Scientific articles: 19
Presentations: 4

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This page:2218
Abstract pages:4009
Full texts:1834
Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 12.04.1940
E-mail: ,
Keywords: optimal control for systems under stochastic forces; problems of spectral optimization; optimal control in elliptic systems; mathematical modeling in biology; stability in nonconservative problems.


Problem of spectral optimization for elastic systems and its application to the problems of optimal design of structures was investigated. Solution of some Gamilton–Jacoby–Bellman equation which appears in problems of optimal control of systems under stochastic forces was obtained. Mathematical investigation of Ziegler paradox in mechanics of nonconservative systems was done. Mathematical model of interactions of pollution and environment was obtained.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1966 (department of differential equations). Ph. D. thesis was defended in 1972. D. Sci. thesis was defended in 1988. A list of my works contains more then 100 titles. Since 1998 I have led the research seminar at MSU on mathematical models in biology.

Since 1994 to 1996 I was a scientific program director of Science International Foundation (Soros Foundation); in 1999 I was a visiting professor in Worcester Polytechnic Institute (USA).

Main publications:
  • Bratus' A. S. Condition of extremum for eigenvalues of elliptic boundary-value problems // J. Optimiz. Theory Appl., 1991, 68(3), 432–436.
  • Bratus' A. S., Myshkis A. D. Extremum problems for Laplacian eigenvalues with free boundary // Nonlinear Analysis. Theory, Methods and Application, 1993, 19(9), 815–831.
  • Bratus' A. S. On various cases of instability for elastic nonconservative systems with damping // Int. J. Solid Structures, 1993, 30(24) 3431–3441.
  • Bratus' A. S., Posvyanskii V. P. The optimum shape of a bending beam // J. Appl. Math. Mech., 2000, 64(3), 993–1004.
  • Bratus' A. S., Dimentberg M. F. Bounded parametric control of random vibrations // Proc. R. Soc. Lond, 2000, 456, 2351–2363.
List of publications on Google Scholar

Publications in Math-Net.Ru
1. S. Yu. Kovalenko, A. S. Bratus', “Up and Down Estimate of Therapy Quality in Non-Linear Distributed Mathematical Glioma Model”, Mat. Biolog. Bioinform., 9:1 (2014),  20–32  mathnet
2. S. Yu. Kovalenko, A. S. Bratus', “The task of search viable therapy strategy for a mathematical spatial cancer model”, Computer Research and Modeling, 5:4 (2013),  749–765  mathnet
3. A. S. Bratus', M. V. Safro, “Asymptotics of Eigenvalues of the Jacobi Matrix of a System of Semilinear Parabolic Equations”, Mat. Zametki, 89:2 (2011),  204–213  mathnet  mathscinet; Math. Notes, 89:2 (2011), 206–213  isi  scopus
4. A. V. Antipov, A. S. Bratus', “Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor”, Zh. Vychisl. Mat. Mat. Fiz., 49:11 (2009),  1907–1919  mathnet; Comput. Math. Math. Phys., 49:11 (2009), 1825–1836  isi  scopus
5. A. S. Bratus', E. S. Chumerina, “Optimal control synthesis in therapy of solid tumor growth”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008),  946–966  mathnet  zmath; Comput. Math. Math. Phys., 48:6 (2008), 892–911  isi  scopus
6. A. S. Bratus', A. P. Ivanova, J. Menaldi, D. V. Yurchenko, “Local solutions of the Hamilton–Jacobi–Bellman equation for some stochastic problems”, Avtomat. i Telemekh., 2007, 6,  99–115  mathnet  mathscinet  zmath; Autom. Remote Control, 68:6 (2007), 1023–1038  scopus
7. A. S. Bratus', V. P. Posvyanskii, “Stationary solutions in a closed distributed Eigen–Schuster evolution system”, Differ. Uravn., 42:12 (2006),  1686–1698  mathnet  mathscinet; Differ. Equ., 42:12 (2006), 1762–1774
8. A. S. Bratus', A. L. Khalin, “A method for detection of Hopf bifurcation points”, Zh. Vychisl. Mat. Mat. Fiz., 42:3 (2002),  336–350  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 42:3 (2002), 321–334
9. A. S. Bratus', A. D. Myshkis, “The relation between the first and second natural frequencies of vibrations of a membrane”, Zh. Vychisl. Mat. Mat. Fiz., 32:2 (1992),  320–325  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 32:2 (1992), 264–269  isi
10. N. V. Banichuk, A. S. Bratus', A. D. Myshkis, “Destabilizing action of small dissipative forces on nonconservative systems”, Dokl. Akad. Nauk SSSR, 309:6 (1989),  1325–1327  mathnet  mathscinet  zmath; Dokl. Math., 34:12 (1989), 1068–1070
11. A. S. Bratus', A. D. Myshkis, “The conditions for an extremum in spectral isoperimetric problems with variable boundary”, Zh. Vychisl. Mat. Mat. Fiz., 27:12 (1987),  1790–1801  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 27:6 (1987), 122–129
12. A. S. Bratus', “Multiple eigenvalues in problems of optimization of spectral properties of systems with a finite number of degrees of freedom”, Zh. Vychisl. Mat. Mat. Fiz., 26:5 (1986),  645–654  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 26:3 (1986), 1–7
13. A. S. Bratus', “Sufficient conditions for an extremum in problems of controlling the coefficients of elliptic operators”, Uspekhi Mat. Nauk, 40:2(242) (1985),  171–172  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:2 (1985), 207–208  isi
14. A. S. Bratus', A. P. Seyranian, “Double eigenvalues in optimization problems”, Dokl. Akad. Nauk SSSR, 272:2 (1983),  275–278  mathnet  mathscinet  zmath
15. A. S. Bratus', “Asymptotic solutions in problems of the optimal control of the coefficients of elliptic operators”, Dokl. Akad. Nauk SSSR, 259:5 (1981),  1035–1038  mathnet  mathscinet  zmath
16. A. S. Bratus', V. B. Kolmanovskii, “Approximate optimal control of motion under the action of Poisson and Gaussian random perturbations”, Differ. Uravn., 13:9 (1977),  1558–1569  mathnet  mathscinet  zmath
17. A. S. Bratus', F. L. Chernous'ko, “Numerical solution of problems of optimal correction under random perturbations”, Zh. Vychisl. Mat. Mat. Fiz., 14:1 (1974),  68–78  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 14:1 (1974), 69–79
18. A. S. Bratus', “Estimates in $L_2$ for pseudodifferential operators with a parameter of principal type and their applications to equations in tube domains”, Dokl. Akad. Nauk SSSR, 203:4 (1972),  738–741  mathnet  mathscinet  zmath
19. A. S. Bratus', “A priori estimates for equations with a parameter”, Dokl. Akad. Nauk SSSR, 192:6 (1970),  1202–1205  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Replicators System and Models of Natural Evolution
A. S. Bratus'
Principle Seminar of the Department of Probability Theory, Moscow State University
February 14, 2018 16:45
2. Optimal Synthesis in Stochastic Problems with the Control in the Noise and its Applications to Mechanics and Financial Mathematics Problems
A. S. Bratus'
Principle Seminar of the Department of Probability Theory, Moscow State University
May 18, 2016 16:45
3. Limit behavior of the distributed replicator systems
A. S. Bratus'
International Conference "Irreversibility Problem in Classical and Quantum Dynamical Systems"
December 9, 2011 14:30
4. Предельное поведение распределенных репликаторных систем
A. S. Bratus'
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
April 13, 2011 12:00

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