optimal control for systems under stochastic forces; problems of spectral optimization; optimal control in elliptic systems; mathematical modeling in biology; stability in nonconservative problems.
Subject:
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.
Biography
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.
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
2013
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
2011
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; Math. Notes, 89:2 (2011), 206–213
2009
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; Comput. Math. Math. Phys., 49:11 (2009), 1825–1836
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; Comput. Math. Math. Phys., 48:6 (2008), 892–911
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, no. 6, 99–115; Autom. Remote Control, 68:6 (2007), 1023–1038
A. S. Bratus', V. P. Posvyanskii, “Stationary solutions in a closed distributed Eigen–Schuster evolution system”, Differ. Uravn., 42:12 (2006), 1686–1698; Differ. Equ., 42:12 (2006), 1762–1774
A. S. Bratus', A. L. Khalin, “A method for detection of Hopf bifurcation points”, Zh. Vychisl. Mat. Mat. Fiz., 42:3 (2002), 336–350; Comput. Math. Math. Phys., 42:3 (2002), 321–334
1992
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; Comput. Math. Math. Phys., 32:2 (1992), 264–269
1989
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; Dokl. Math., 34:12 (1989), 1068–1070
1987
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; U.S.S.R. Comput. Math. Math. Phys., 27:6 (1987), 122–129
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; U.S.S.R. Comput. Math. Math. Phys., 26:3 (1986), 1–7
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; Russian Math. Surveys, 40:2 (1985), 207–208
1983
14.
A. S. Bratus', A. P. Seyranian, “Double eigenvalues in optimization problems”, Dokl. Akad. Nauk SSSR, 272:2 (1983), 275–278
1981
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
1977
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
1974
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; U.S.S.R. Comput. Math. Math. Phys., 14:1 (1974), 69–79
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
1970
19.
A. S. Bratus', “A priori estimates for equations with a parameter”, Dokl. Akad. Nauk SSSR, 192:6 (1970), 1202–1205
Nonlinear wave in hypercycle with infinity many members A. S. Bratus' III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 5, 2023 14:30
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