01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
28.03.1958
E-mail:
Keywords:
Lopatinsky condition,
Lyapunov stability,
viscous heatconducting gas,
well-posedness,
a shock wave,
the hyperbolic equations and systems,
Boltzmann еquation,
hydrodynamical models of carry of a charge in semiconductors,
Sobolev-type system,
weakened solution,
local- and global-in-time existence,
Lyapunov's asymptotic stability,
stabilization method.
UDC:
517.95, 517.956.3, 517.958, 517.956
Subject:
Boundary problems for equations and systems of the equations in partial derivatives in domains with nonsmooth boundary, problems of a flow for ideal, viscous heatconducting gases, the description of carry of a charge in semiconductors, systems of conservation laws.
Biography
EDUCATION
1999 Doctor of Science (the higher, post-doctorate degree) in Differential Equations and Mathematical Physics, Novosibirsk State University, Novosibirsk, Russia
1988 Ph.D. in Differential Equations and Mathematical Physics, Novosibirsk State University, Novosibirsk, Russia
1985–1988 Post-graduate studies in Differential Equations and Mathematical Physics, Novosibirsk State University, Novosibirsk, USSR
1982–1985 Probation period in Novosibirsk State University, Novosibirsk, USSR
1979 Diploma (= M.S.) in Differential Equations and Mathematical Physics, Novosibirsk State University, Novosibirsk, USSR
PROFESSIONAL AND ACADEMIC EXPERIENCE
2000–present Novosibirsk State University, Professor of Differential Equations
1995–2000 Novosibirsk State University, Associate Professor of Differential Equations
1989–1995 Novosibirsk State University, Senior research worker
2001–present Novosibirsk Institute of Mathematics Russian Academy of Sciences, Siberian Branch, Leading research worker.
Main publications:
A. M. Blokhin, D. L. Tkachev, Mixed problems for the wave equation in coordinate domains, Nova Science Publishers, Inc., New York, 1998, 133 p.
A. M. Blokhin, D. L. Tkachev, Yu. Yu. Pashinin, “Stability of shock waves in the problem of flowing around an infinite planar wedge: the case of strong shock”, Proceedings of the International Conference “Eleventh International Conference on Hyperbolic Problems. Theory. Numerics. Applications” (Lyon, France, July 17–21, 2006), 1037–1045
A. M. Blokhin, D. L. Tkachev, L. O. Baldan, “Study of the stability in the problem on flowing around a wedge. The case of strong wave”, Mathematical Analysis and Applications, 319 (2006), 248–277
A. M. Blokhin, D. L. Tkachev, L. O. Baldan, “Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. Part I”, Mathematical Analysis and Applications, 331 (2007), 408–423
A. M. Blokhin, D. L. Tkachev, D. V. Esipov, “Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. Part II”, Mathematical Analysis and Applications, 331 (2007), 424–442
A. M. Blokhin, D. L. Tkachev, Yu. Yu. Pashinin, “Stability condition for the strong shock wave in the problem on flow around infinite plane wedge”, Nonlinear Analysis. Hybrid Systems, 2:1 (2008), 1–17
A. M. Blokhin. D. L. Tkachev, “Representation of the solution to a model problem in semiconductor physics”, Mathematical Analysis and Applications, 341 (2008), 1468–1475
D. L. Tkachev, E. A. Biberdorf, “Spectrum of a problem about the flow of a polymeric viscoelastic fluid in a cylindrical channel (Vinogradov-Pokrovski model)”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1269–1289
2.
D. L. Tkachev, “The spectrum and Lyapunov linear instability of the stationary state for polymer fluid flows: the Vinogradov–Pokrovskii model”, Sibirsk. Mat. Zh., 64:2 (2023), 423–440; Siberian Math. J., 64:2 (2023), 407–423
A. M. Blokhin, D. L. Tkachev, “Lyapunov instability of stationary flows of a polymeric fluid in a channel with perforated walls”, Mat. Sb., 213:3 (2022), 3–20; Sb. Math., 213:3 (2022), 283–299
A. M. Blokhin, D. L. Tkachev, “Линейная неустойчивость состояния покоя для МГД модели несжимаемой полимерной жидкости в случае абсолютной проводимости”, Mat. Tr., 24:1 (2021), 35–51
A. M. Blokhin, A. S. Rudometova, D. L. Tkachev, “An MHD model of an incompressible polymeric fluid:
linear instability of a steady state”, Sib. Zh. Ind. Mat., 23:3 (2020), 16–30; J. Appl. Industr. Math., 14:3 (2020), 430–442
6.
A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type flows in an MHD model of an incompressible polymeric fluid”, Mat. Sb., 211:7 (2020), 3–23; Sb. Math., 211:7 (2020), 901–921
A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in the infinite channel”, Prikl. Mekh. Tekh. Fiz., 59:6 (2018), 39–51; J. Appl. Mech. Tech. Phys., 59:6 (2018), 992–1003
A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Local solvability of the problem of the van der Waals gas flow around an infinite plane wedge in the case of a weak shock wave”, Sibirsk. Mat. Zh., 59:6 (2018), 1214–1239; Siberian Math. J., 59:6 (2018), 960–982
A. M. Blokhin, A. V. Yegitov, D. L. Tkachev, “Asymptotics of the spectrum of a linearized problem of the stability of a stationary flow of an incompressible polymer fluid with a space charge”, Zh. Vychisl. Mat. Mat. Fiz., 58:1 (2018), 108–122; Comput. Math. Math. Phys., 58:1 (2018), 102–117
A. M. Blokhin, D. L. Tkachev, “Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave”, Mat. Tr., 19:2 (2016), 3–41; Siberian Adv. Math., 27:2 (2017), 77–102
2015
11.
A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Linear instability of the solutions in mathematical model that describe flows of polymer in an infinite channel”, Yakutian Mathematical Journal, 22:2 (2015), 16–27
12.
A. M. Blokhin, A. V. Yegitov, D. L. Tkachev, “Linear instability of solutions in a mathematical model describing polymer flows in an infinite channel”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 850–875; Comput. Math. Math. Phys., 55:5 (2015), 848–873
A. M. Blokhin, D. L. Tkachev, “Linear asymptotic instability of a stationary flow of a polymeric medium in a plane channel in the case of periodic perturbations”, Sib. Zh. Ind. Mat., 17:3 (2014), 13–25; J. Appl. Industr. Math., 8:4 (2014), 467–478
A. M. Blokhin, D. L. Tkachev, “Regularity of the solution and well-posedness of a mixed problem for an elliptic system with quadratic nonlinearity in gradients”, Zh. Vychisl. Mat. Mat. Fiz., 52:10 (2012), 1866–1882; Comput. Math. Math. Phys., 52:10 (2012), 1428–1444
2011
15.
A. M. Blokhin, D. L. Tkachev, “Justification of the stabilization method for a mathematical model of charge transport in semiconductors”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1495–1517; Comput. Math. Math. Phys., 51:8 (2011), 1395–1417
2009
16.
A. M. Blokhin, D. L. Tkachev, “Stability of a supersonic flow about a wedge with weak shock wave”, Mat. Sb., 200:2 (2009), 3–30; Sb. Math., 200:2 (2009), 157–184
A. M. Blokhin, D. L. Tkachev, “A mixed problem for the wave equation in a domain with a corner (the scalar case)”, Sibirsk. Mat. Zh., 30:3 (1989), 16–23; Siberian Math. J., 30:3 (1989), 358–364
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