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Sibirskii Zhurnal Industrial'noi Matematiki
2015, vol. 18, No 1 (61)Contents
UDC 519.634
DOI 10.17377/sibjim.2015.18.101
Blokhin A.M., Rudometova A.S.
Stationary solutions to the equations describing the nonisothermic electrical convection of a weak-conductive incompressible polymeric fluidA mathematical model describing flows of a weak-conductive polymeric fluid in a horizontal condenser (channel) is created. Stationary solutions to this model are found.
Keywords: incompressible polymeric fluid, nonisothermic flow, stationary flow of polymeric fluid.
Pp. 3–13.Blokhin Alexander Mikhailovich
Rudometova Anna Sergeevna
Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk;
Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk. E-mail: blokhin@math.nsc.ru; bush@math.nsc.ru
UDC 519.833:339.144
DOI 10.17377/sibjim.2015.18.102
Gasratova N.A., Gasratov M.G.
A network inventory control model in the case of quantitative competitionUnder study is a mathematical model of processes of cyclic transportation in logistic systems for the case of quantitative competition. We consider a network of a set of stations at each of which there are several enterprises with their warehouses. Enterprises supply and sell homogeneous products the demand for which is deterministic. Each enterprise uses a relaxation method of inventory control with the assumption of deficiency when modeling control systems. Existence conditions for an equilibrium solution for the model are given.
Keywords: logistic system, quantitative competition, internal strategy, external strategy, Nash equilibrium in pure strategy, inventory control.
Pp.14–27.Gasratova Natalia Alexandrovna
St. Petersburg State University, 7-9, Universitetskaya emb. 199034 St. Petersburg. E-mail: gasratova_na@mail.ru
Gasratov Mansur Gabibullakhovich
OJSC MegaFon E-mail: gasratovmans@mail.ru
UDC 517.957
DOI 10.17377/sibjim.2015.18.103
Kaliev I.A., Shukhardin A.A., Sabitova G.S.
An ingression problem for the systems of equations of a viscous heat-conducting gas in time-increasing noncylindrical domainsThe global solvability of an ingression problem for the complete system of equations describing one-dimensional nonstationary flow of a viscous heat-conducting gas in time-increasing noncylindrical domains is proved. The proof of the existence and uniqueness theorem of the total solution with respect to time is connected with obtaining a priori estimates in which the constants depend only on the data of the problem and the length of the time interval T but do not depend on the existence interval of a local solution.
Keywords: system of the Navier—Stokes equations, heat-conducting gas, global solvability, time-increasing non-cylindrical domains.
Pp. 28–44.Kaliev Ibragim Adietovich
Sabitova Gulnara Sagyndykovna
Shukhardin Andrey Aleksandrovich
Sterlitamak Branch of Bashkir State University, 37 Lenin av., 453103 Sterlitamak. E-mail: kalievia@mail.ru; shukhardinaa@gmail.com; sabitovags@mail.ru
UDC 519.633.2:519.642.5
DOI 10.17377/sibjim.2015.18.104
Karchevskii A.L., Nazarov L.A., Nazarova L.A.
Calculation of gas pressure in a closed vessel with coal slack under isothermal desorptionWe present an algorithm for calculating the concentration of methane from coal slack placed in a hermetically closed container. The algorithm allows calculating the values of methane concentration for large times.
Keywords: parabolic equation, Volterra integral equation, canister test, methane concentration, coal slack.
Pp. 45–55.Karchevskii Andrey Leonidovich
Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
Nazarov Leonid Anatol'evich
Nazarova Larisa Alekseevna
Chinacal Institute of Mining SB RAS, 54 Krasnyi av., 630091 Novosibirsk. E-mail: karchevs@math.nsc.ru; naz@misd.nsc.ru
UDC 681.511.2
DOI 10.17377/sibjim.2015.18.105
Koryukin A.N., Voevoda A.A.
PID controllers of a two-mass system and complex pairs of multiplicity 2We study the stability of a one-channel two-mass system controlled by a proportional integral differential (PID) controller. The controlling force is applied only to one of the masses and the output is the deviation of this mass. It is shown that, among PID controllers, the greatest stability is provided by the regulators for which the right vertical of the roots of the characterisitc polynomial contains a complex pair of multiplicity 2.
Keywords: modal synthesis, lowered-order regulator, greatest stability degree, maximum stability degree, limit stability degree.
Pp. 56–68Koryukin Anatolii Nikolaevich
Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk. E-mail: koryukin@sibmail.ru
Voevoda Aleksandr Aleksandrovich
Novosibirsk State Technical University, 20 Karl Marx av. 630073 Novosibirsk. E-mail: ucit@ucit.ru
UDC 517.946
DOI 10.17377/sibjim.2015.18.106
Kosov A., Semenov E., Sinitsyn A.
Constructing solutions to systems of nonlinear equations for magnetic insulation modellingWe consider a model of magnetic insulation in a plane diode which is presented as a system of two nonlinear second-order ODE. Integrability of the model is justified and a method for solving a singular boundary value problem is developed. We propose a generalized model of magnetic insulation with multidimensional Laplace operator, which is the principal object of study in this paper. We obtain conditions under which exact solutions to the boundary value problem for a spherical layer are found.
Keywords: singular boundary value problem, integrability, elliptic type equation, exact solution.
Pp. 69–83.Kosov Aleksandr Arkadievich
Semenov Eduard Ivanovich
Institute for System Dynamics and Control Theory SB RAS, 134 Lermontov st., 664033 Irkutsk. E-mail: kosov_idstu@mail.ru; edwseiz@gmail.com
Sinitsyn Aleksandr Vladimirovich
Universidad Nacional de Colombia, Carrera 45, Bogota, Colombia. E-mail: avsinitsyn@yahoo.com
UDC 519.63:532.13
DOI 10.17377/sibjim.2015.18.107
Kuliev S.Z.
An approach to the determination of the hydraulic resistance coefficient for a pipeline section under an unsteady flow regimeThe article is devoted to the determination of the value of the hydraulic resistance coefficient of a linear section of a main pipeline. The problem under consideration is reduced to a finite-dimensional optimization problem, for solving which we propose to use first-order numerical methods. We deduce formulas for the components of the gradient of the objective functional in the space of identifiable parameters. The results of the implemented numerical experiments are given.
Keywords: hyperbolic equation, hydraulic resistance coefficient, inverse problem, first-order optimization method, adjoint problem, gradient of a functional
Pp. 84–94.Kuliev Samir Zakir
Institute of Cybernetics of the Azerbaijan National Academy of Sciences, 9, B.Vahabzade st., AZ 1141 Baku, Azerbaijan. E-mail: kamil_aydazade@rambler.ru; copal@box.az
UDC 533.6.011.51
DOI 10.17377/sibjim.2015.18.108
Markovskii A.I.
On the identification of the reservoir pressures and filtration coefficients of two gas-bearing formations opened by one well from pressure and debit measurements on the mouthWe consider the problem of the determination of the unknown filtration coefficients and formation pressures for two formations exploited together by one well from the measurements on the stationary regimes of the pressure and the total debit on the mouth of the well. The problem is reduced to solving a complex system of three nonlinear equations. We construct an algorithm for its numerical solution and its computer realization for one of the possible variants. An example of numerical solution is given.
Keywords: gas filtration, supercompressibility, connected formations, well and formation debits, turning point, Newton method
Pp. 95–109.Markovskii Anatolii Ivanovich
Institute of Applied Mathematics and Mechanics NAS Ukraine, 74, R. Luxemburg st., 83114 Donetsk, Ukraine E-mail: markowski@yandex.ru
UDC 517.977.54
DOI 10.17377/sibjim.2015.18.109
Rokhlin D.B., Mironenko G. V.
Calcilating optimal dividend payment, reinsurance, and investment strategies in a diffusion modelWe consider the problem of the maximization of the total expected discounted amount of dividends paid by an insurance company up to the bankruptcy. It is assumed that the reinsurance is allowed and the wealth can be invested in a risky asset whose dynamics is described by the Black–Scholes model with random drift obeying the Ornstein–Uhlenbeck process. In accordance with the general scheme of dynamic programming, the problem is reduced to solving a Dirichlet problem for the corresponding Hamilton–Jacobi–Bellman equation in the half-plane. The problem is solved numerically by means of a monotone finite-difference scheme, which is proved to converge to a unique viscosity solution of the mentioned equation. We present and discuss the results of numerical experiments which indicate some nontrivial properties of optimal strategies.
Keywords: Hamilton–Jacobi–Bellman equation, viscosity solution, monotone scheme, dividend, reinsurance, investment, random factor
Pp. 110–122,Rokhlin Dmitrii Borisovich
Mironenko Georgii Viktorovich
Southern Federal University, 8a Mil'chakova st., 344090 Rostov-on-Don. E-mail: rokhlin@math.rsu.ru, georim89@mail.ru
UDC 536.516
DOI 10.17377/sibjim.2015.18.110
Sennitskii V. L.
On a prescribed orientation of a solid inclusion in a viscous fluidWe pose and solve a problem of the rotational motion of a solid inclusion in an oscillating viscous fluid. The new hydromechanical effect is revealed: under any (perturbed) initial position of the inclusion, there happens its subsequent ``spontaneous'' passage into one of the two stable equilibria corresponding to the orientation of the inclusion along the oscillation axis of the fluid.
Keywords: viscous fluid, solid body, inclusion, oscillation, field of gravity, method of averaging.
Pp. 123–128.Sennitskii Vladimir Leonidovich
Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk 630090 Novosibirsk