01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
12.06.1945
E-mail:
Keywords:
Navier–Stokes equations; mathematical problems of statistical hydrodynamics, optimal control of distributed parameter systems, controllability and feedback stabilization for parabolic equatons and for Navier–Stokes system.
Main publications:
Fursikov A. V. Stabiliziruemost kvazilineinogo parabolicheskogo uravneniya s pomoschyu granichnogo upravleniya s obratnoi svyazyu // Matem. sbornik, 2001, 192(4), 115–160.
Fursikov A. V. Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya. Nauchnaya kniga, Novosibirsk, 1999, 350 s.
Fursikov A. V., Emanuilov O. Yu. Tochnaya upravlyaemost uravnenii Nave–Stoska i Bussineska // Uspekhi matem. nauk, 1999, 54(3), 93–146.
Fursikov A. V. Momentnaya teoriya dlya uravnenii Nave–Stoksa so sluchainoi pravoi chastyu // Izvestiya RAN. Ser. matem., 1992, 56, 1273–1315.
Vishik M. I., Fursikov A. V. Matematicheskie zadachi statisticheskoi gidromekhaniki. Nauka, Moskva, 1980, 440 s.
A. A. Vasil'eva, A. V. Gorshkov, M. P. Zapletin, L. V. Lokutsievskiy, G. G. Magaril-Il'yaev, K. Yu. Osipenko, K. S. Ryutin, A. V. Fursikov, “Main recent research results of the staff of the Chair of General Problems of Control”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 6, 64–71; Moscow University Mathematics Bulletin, 79:6 (2024), 351–359
2014
2.
A. V. Fursikov, L. S. Shatina, “On an estimate connected with the stabilization of normal parabolic equation by start control”, Fundam. Prikl. Mat., 19:4 (2014), 197–230; J. Math. Sci., 217:6 (2016), 803–826
A. V. Fursikov, “Flow of a viscous incompressible fluid around a body: boundary-value problems and minimization of the work of a fluid”, CMFD, 37 (2010), 83–130; Journal of Mathematical Sciences, 180:6 (2012), 763–816
A. V. Fursikov, “Stabilization from the boundary of solution for Navier-Stokes system: solvability and justification of numerical simulation”, Dal'nevost. Mat. Zh., 4:1 (2003), 86–100
A. V. Fursikov, “Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback”, Mat. Sb., 192:4 (2001), 115–160; Sb. Math., 192:4 (2001), 593–639
A. V. Fursikov, O. Yu. Imanuvilov, “Exact controllability of the Navier–Stokes and Boussinesq equations”, Uspekhi Mat. Nauk, 54:3(327) (1999), 93–146; Russian Math. Surveys, 54:3 (1999), 565–618
A. V. Fursikov, Yu. S. Èmanuilov, “Local exact controllability of the two-dimensional Navier–Stokes equations”, Mat. Sb., 187:9 (1996), 103–138; Sb. Math., 187:9 (1996), 1355–1390
A. V. Fursikov, O. Yu. Imanuvilov, “Rate of convergence in the closure of a chain of moment equations that correspond to the Navier–Stokes system with a random right-hand side”, Differ. Uravn., 30:4 (1994), 699–711; Differ. Equ., 30:4 (1994), 646–658
9.
A. V. Fursikov, O. Yu. Imanuvilov, “The rate of convergence of approximations for the closure of the Friedman–Keller chain in the case of large Reynolds numbers”, Mat. Sb., 185:2 (1994), 115–143; Russian Acad. Sci. Sb. Math., 81:1 (1995), 235–259
A. V. Fursikov, “Moment theory for the Navier–Stokes equations with a random right side”, Izv. RAN. Ser. Mat., 56:6 (1992), 1273–1315; Russian Acad. Sci. Izv. Math., 41:3 (1993), 515–555
A. V. Fursikov, O. Yu. Imanuvilov, “On $\varepsilon$-controllability of the Stokes problem with distributed control concentrated on a subdomain”, Uspekhi Mat. Nauk, 47:1(283) (1992), 217–218; Russian Math. Surveys, 47:1 (1992), 255–257
A. V. Fursikov, “The problem of closure of the chains of moment equations corresponding to the three-dimensional Navier–Stokes system in the case of large Reynolds numbers”, Dokl. Akad. Nauk SSSR, 319:1 (1991), 83–87; Dokl. Math., 44:1 (1992), 80–85
A. V. Fursikov, “The Cauchy problem for a second-order elliptic equation in a conditionally well-posed formulation”, Tr. Mosk. Mat. Obs., 52 (1989), 138–174
A. V. Fursikov, “On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system”, Mat. Sb. (N.S.), 134(176):4(12) (1987), 472–495; Math. USSR-Sb., 62:2 (1989), 465–490
A. Romanovich, A. V. Fursikov, “On the question of the solvability of the Cauchy problem for the Laplace operator”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 3, 78–80
1986
16.
A. V. Fursikov, “Analytic functionals and unique solvability of quasilinear dissipative systems under almost all initial conditions”, Tr. Mosk. Mat. Obs., 49 (1986), 3–55
A. V. Fursikov, “Space-time moments and statistical solutions concentrated on smooth solutions of a three-dimensional Navier–Stokes system or a quasilinear parabolic system”, Dokl. Akad. Nauk SSSR, 274:3 (1984), 548–553
A. V. Fursikov, “Solvability of a chain of equations for space-time moments”, Mat. Sb. (N.S.), 125(167):3(11) (1984), 306–331; Math. USSR-Sb., 53:2 (1986), 307–334
A. V. Fursikov, “Properties of solutions of some control problems connected with the Navier–Stokes system”, Dokl. Akad. Nauk SSSR, 262:1 (1982), 44–48
20.
A. V. Fursikov, “Properties of solutions of some extremal problems connected with the Navier–Stokes system”, Mat. Sb. (N.S.), 118(160):3(7) (1982), 323–349; Math. USSR-Sb., 46:3 (1983), 323–351
A. V. Fursikov, “On the problem of unique solubility of a three-dimensional Navier–Stokes system for almost all initial conditions”, Uspekhi Mat. Nauk, 36:2(218) (1981), 207–208; Russian Math. Surveys, 36:2 (1981), 169–170
22.
A. V. Fursikov, “Control problems and theorems concerning the unique solvability of a mixed boundary value problem for the three-dimensional Navier–Stokes and Euler equations”, Mat. Sb. (N.S.), 115(157):2(6) (1981), 281–306; Math. USSR-Sb., 43:2 (1982), 251–273
A. V. Fursikov, “On some control problems and results concerning the unique solvability of a mixed boundary value problem for the
three-dimensional Navier–Stokes and Euler systems”, Dokl. Akad. Nauk SSSR, 252:5 (1980), 1066–1070
M. I. Vishik, A. I. Komech, A. V. Fursikov, “Some mathematical problems of statistical hydromechanics”, Uspekhi Mat. Nauk, 34:5(209) (1979), 135–210; Russian Math. Surveys, 34:5 (1979), 149–234
M. I. Vishik, A. V. Fursikov, “Space-time statistical solutions of the Navier-Stokes system which are homogeneous in $x$, and individual solutions with infinite energy”, Dokl. Akad. Nauk SSSR, 239:5 (1978), 1025–1028
M. I. Vishik, A. V. Fursikov, “Translationally homogeneous statistical solutions and individual solutions with infinite energy of a system of Navier–Stokes equations”, Sibirsk. Mat. Zh., 19:5 (1978), 1005–1031; Siberian Math. J., 19:5 (1978), 710–729
M. I. Vishik, A. V. Fursikov, “Homogeneous statistical solutions of the Navier–Stokes system”, Uspekhi Mat. Nauk, 32:5(197) (1977), 179–180
1976
28.
M. I. Vishik, A. V. Fursikov, “The Cauchy problem for the Hopf equation corresponding to parabolic equations. Statistical solutions and moment functions”, Dokl. Akad. Nauk SSSR, 227:5 (1976), 1041–1044
A. V. Fursikov, “Formulas for certain functionals of the smooth solutions of a class of systems of quasilinear equations”, Uspekhi Mat. Nauk, 31:1(187) (1976), 265–266
1975
30.
M. I. Vishik, A. V. Fursikov, “The Cauchy problem for nonlinear Schrödinger-type equations”, Mat. Sb. (N.S.), 96(138):3 (1975), 458–470; Math. USSR-Sb., 25:3 (1975), 429–440
M. I. Vishik, A. V. Fursikov, “Analytic first integrals of non-linear parabolic systems of differential equations in the sense of Petrovskii, and applications”, Uspekhi Mat. Nauk, 29:2(176) (1974), 123–153; Russian Math. Surveys, 29:2 (1974), 124–157
M. I. Vishik, A. V. Fursikov, “Asymptotic expansion of moment functions of solutions of nonlinear parabolic equations”, Mat. Sb. (N.S.), 95(137):4(12) (1974), 588–605; Math. USSR-Sb., 24:4 (1974), 575–591
M. I. Vishik, A. V. Fursikov, “Some questions in the theory of nonlinear elliptic and parabolic equations”, Mat. Sb. (N.S.), 94(136):2(6) (1974), 300–334; Math. USSR-Sb., 23:2 (1974), 287–318
M. I. Vishik, A. V. Fursikov, “Analytic first integrals of nonlinear parabolic equations and their applications”, Mat. Sb. (N.S.), 92(134):3(11) (1973), 347–377; Math. USSR-Sb., 21:3 (1973), 339–369
A. R. Alimov, A. A. Vasil'eva, S. V. Konyagin, A. S. Kochurov, A. I. Kozko, T. P. Lukashenko, K. S. Ryutin, V. M. Tikhomirov, A. V. Fursikov, V. N. Chubarikov, “Igor Germanovich Tsarkov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 70–71
2013
40.
M. S. Agranovich, A. V. Babin, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, S. B. Kuksin, A. P. Kuleshov, V. P. Maslov, S. P. Novikov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirelman, M. A. Shubin, G. I. Eskin, “Marko Iosifovich Vishik (obituary)”, Uspekhi Mat. Nauk, 68:2(410) (2013), 197–200; Russian Math. Surveys, 68:2 (2013), 383–387
2008
41.
A. V. Fursikov, “Sergey L'vovich Sobolev (to his 100-th Anniversary)”, Math. Ed., 2008, no. 2(46), 8–15
2007
42.
C. E. Wayne, P. Gerard, W. Craig, S. B. Kuksin, A. G. Sergeev, A. V. Fursikov, “Workshop on Mathematical Hydrodynamics”, Uspekhi Mat. Nauk, 62:3(375) (2007), 3–4; Russian Math. Surveys, 62:3 (2007), 407–408
1997
43.
M. S. Agranovich, A. V. Babin, L. R. Volevich, A. Yu. Goritskii, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, M. L. Krasnov, S. B. Kuksin, G. I. Makarenko, V. P. Maslov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirel'man, M. A. Shubin, “Mark Iosifovich Vishik (on his 75th birthday)”, Uspekhi Mat. Nauk, 52:4(316) (1997), 225–232; Russian Math. Surveys, 52:4 (1997), 853–861
1975
44.
É. Dzhusti, M. I. Vishik, A. V. Fursikov, A. S. Schwarz, O. I. Bogoyavlenskii, B. M. Levitan, V. V. Kucherenko, A. G. Kushnirenko, M. V. Fedoryuk, M. A. Shubin, A. D. Bruno, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 30:2(182) (1975), 261–269
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