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Zlotnik, Alexander A.

Author ID: zlotnik.alexander-a Recent zbMATH articles by "Zlotnik, Alexander A."
Published as: Zlotnik, A. A.; Zlotnik, Alexander; Zlotnik, A.; Zlotnik, Alexander A.; Złotnik, A. A.
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Serials

33 Doklady Mathematics
15 Computational Mathematics and Mathematical Physics
14 Mathematical Notes
10 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
10 Applied Mathematics Letters
10 Russian Journal of Numerical Analysis and Mathematical Modelling
9 Soviet Mathematics. Doklady
6 Russian Mathematics
6 Soviet Journal of Numerical Analysis and Mathematical Modelling
6 Mathematical Modelling and Analysis
5 Differential Equations
5 U.S.S.R. Computational Mathematics and Mathematical Physics
5 Matematicheskoe Modelirovanie
5 Computational Methods in Applied Mathematics
4 Moscow University Computational Mathematics and Cybernetics
4 Differential Equations
4 Kinetic and Related Models
3 Mathematical Methods in the Applied Sciences
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Communications in Mathematical Sciences
2 Moscow University Mathematics Bulletin
2 Applied Mathematics and Computation
2 Differentsial’nye Uravneniya
2 Siberian Mathematical Journal
2 Applied Numerical Mathematics
2 Journal of Scientific Computing
2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
2 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika
2 Vychislitel’nye Protsessy i Sistemy
2 Sbornik: Mathematics
2 Abstract and Applied Analysis
1 Archive for Rational Mechanics and Analysis
1 Dinamika Sploshnoĭ Sredy
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Journal of Differential Equations
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Mathematics of the USSR, Sbornik
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Russian Journal of Mathematical Physics
1 Journal of Mathematical Sciences (New York)
1 Journal of Mathematical Fluid Mechanics
1 Journal of Evolution Equations
1 Discrete and Continuous Dynamical Systems. Series B
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Mathematical Control and Related Fields
1 Journal of Computational Dynamics

Publications by Year

Citations contained in zbMATH Open

157 Publications have been cited 1,112 times in 464 Documents Cited by Year
Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations. Zbl 1088.35516
Zlotnik, A. A.
76
2000
Lyapunov functional method for 1D radiative and reactive viscous gas dynamics. Zbl 1070.76044
Ducomet, Bernard; Zlotnik, Alexander
51
2005
On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics. Zbl 1083.35109
Ducomet, Bernard; Zlotnik, Alexander
38
2005
Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them. Zbl 1201.76232
Zlotnik, A. A.; Chetverushkin, B. N.
33
2008
On stability of generalized solutions to the equations of one-dimensional motion of a viscous heat conducting gas. Zbl 0880.35026
Zlotnik, A. A.; Amosov, A. A.
31
1997
Global generalized solutions of the equations of the one-dimensional motion of a viscous heat-conducting gas. Zbl 0850.76595
Amosov, A. A.; Zlotnik, A. A.
30
1988
Solvability ”in the large” of a system of equations of the one- dimensional motion of an inhomogeneous viscous heat-conducting gas. Zbl 0779.76079
Amosov, A. A.; Zlotnik, A. A.
29
1992
Global properties of solutions to 1D-viscous compressible barotropic fluid equations with density dependent viscosity. Zbl 1040.35064
Straškraba, Ivan; Zlotnik, Alexander
27
2003
Convergence rate estimates of finite-element methods for second-order hyperbolic equations. Zbl 0851.65063
Zlotnik, A. A.
21
1994
Energy equalities and estimates for barotropic quasi-gasdynamic and quasi-hydrodynamic systems of equations. Zbl 1224.35356
Zlotnik, A. A.
18
2010
On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force. Zbl 1289.76068
Zlotnik, A. A.
17
2012
Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data. Zbl 1072.35082
Jiang, Song; Zlotnik, Alexander
16
2004
Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations. Zbl 1457.76129
Zlotnik, A. A.
16
2017
Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface. Zbl 1422.65145
Balashov, Vladislav; Zlotnik, Alexander; Savenkov, Evgeny
16
2017
Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system. Zbl 1125.35071
Ducomet, B.; Zlotnik, A.
15
2005
Parabolicity of a quasihydrodynamic system of equations and the stability of its small perturbations. Zbl 1160.35326
Zlotnik, A. A.
15
2008
On equations for one-dimensional motion of a viscous barotropic gas in the presence of a body force. Zbl 0811.76075
Zlotnik, A. A.
14
1992
Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases. Zbl 0917.35109
Zlotnik, A. A.; Amosov, A. A.
14
1998
On a decay rate for 1D-viscous compressible barotropic fluid equations. Zbl 1038.35065
Straškraba, Ivan; Zlotnik, Alexander
14
2002
A difference scheme on a non-uniform mesh for the equations of one- dimensional magnetic gas dynamics. Zbl 0702.76126
Amosov, A. A.; Zlotnik, A. A.
13
1989
Global behavior of 1d-viscous compressible barotropic fluid with a free boundary and large data. Zbl 1042.76050
Straškraba, Ivan; Zlotnik, Alexander
13
2003
Properties and asymptotic behavior of solutions of some problems of one- dimensional motion of a viscous barotropic gas. Zbl 0828.76070
Zlotnik, A. A.; Nguyen Zha Bao
12
1994
Quasi-gasdynamic system of equations with general equations of state. Zbl 1387.35510
Zlotnik, A. A.
12
2010
On a hyperbolic perturbation of a parabolic initial-boundary value problem. Zbl 1524.35281
Chetverushkin, Boris N.; Zlotnik, Alexander A.
12
2018
On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation. Zbl 1195.65106
Ducomet, Bernard; Zlotnik, Alexander; Zlotnik, Ilya
12
2009
Conditions for \(L^2\)-dissipativity of linearized explicit difference schemes with regularization for 1D barotropic gas dynamics equations. Zbl 1461.76354
Zlotnik, A. A.; Lomonosov, T. A.
12
2019
On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force. Zbl 1382.76198
Zlotnik, A. A.
12
2016
Stabilization rate and stability for viscous compressible barotropic symmetric flows with free boundary for a general mass force. Zbl 1151.35432
Zlotnik, A. A.; Ducomet, B.
11
2005
On quasi-gasdynamic and quasi-hydrodynamic equations for binary gas mixtures. Zbl 1315.76028
Elizarova, T. G.; Zlotnik, A. A.; Chetverushkin, B. N.
11
2014
Spatial discretization of the one-dimensional quasi-gasdynamic system of equations and the entropy balance equation. Zbl 1274.35301
Zlotnik, A. A.
11
2012
On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. I. Zbl 1119.65085
Ducomet, B.; Zlotnik, A.
11
2006
Regularized equations for numerical simulation of flows of homogeneous binary mixtures of viscous compressible gases. Zbl 1433.76051
Elizarova, T. G.; Zlotnik, A. A.; Shil’nikov, E. V.
11
2019
Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation. Zbl 1267.65144
Zlotnik, Alexander; Zlotnik, Ilya
10
2012
Stabilization for viscous compressible heat-conducting media equations with nonmonotone state functions. Zbl 1078.35524
Ducomet, Bernard; Zlotnik, Alexander
10
2002
Viscous compressible barotropic symmetric flows with free boundary under general mass force I: Uniform-in-time bounds and stabilization. Zbl 1068.35102
Ducomet, Bernard; Zlotnik, Alexander
10
2005
An energy dissipative spatial discretization for the regularized compressible Navier-Stokes-Cahn-Hilliard system of equations. Zbl 1476.65159
Balashov, Vladislav; Zlotnik, Alexander
10
2020
On conditions for \(L^2\)-dissipativity of linearized explicit QGD finite-difference schemes for one-dimensional gas dynamics equations. Zbl 1408.76396
Zlotnik, A. A.; Lomonosov, T. A.
10
2018
Weak solutions to the equations of motion of viscous compressible reacting binary mixtures: uniqueness and Lipschitz-continuous dependence on data. Zbl 1122.35118
Zlotnik, A. A.
9
2004
Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients. Zbl 1407.65203
Trautmann, Philip; Vexler, Boris; Zlotnik, Alexander
9
2018
Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics. Zbl 1416.76171
Balashov, Vladislav; Savenkov, Evgenii; Zlotnik, Alexander
9
2019
The space discretization of the one-dimensional barotropic quasi-gas dynamic system of equations and the energy balance equation. Zbl 1289.76074
Zlotnik, A. A.
8
2012
Stabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state. Zbl 1160.35491
Ducomet, Bernard; Zlotnik, Alexander
8
2003
On quasi-averaged equations of the one-dimensional motion of a viscous barotropic medium with rapidly oscillating data. Zbl 1027.35504
Amosov, A. A.; Zlotnik, A. A.
8
1996
On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. II. Zbl 1141.65069
Ducomet, B.; Zlotnik, A.
8
2007
On a new spatial discretization for a regularized 3D compressible isothermal Navier-Stokes-Cahn-Hilliard system of equations with boundary conditions. Zbl 1475.65063
Balashov, Vladislav; Zlotnik, Alexander
8
2021
An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier-Stokes-Cahn-Hilliard equations. Zbl 1446.65060
Balashov, Vladislav; Zlotnik, Alexander
8
2020
On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations. Zbl 1407.76106
Zlotnik, A.; Lomonosov, T.
8
2018
Uniform estimates and stabilization of solutions to equations of one-dimensional motion of a multicomponent barotropic mixture. Zbl 0852.76078
Zlotnik, A. A.
7
1995
Uniqueness and stability of generalized solutions for a class of quasilinear systems of composite type equations. Zbl 0832.35102
Amosov, A. A.; Zlotnik, A. A.
7
1994
The Numerov-Crank-Nicolson scheme on a non-uniform mesh for the time-dependent Schrödinger equation on the half-axis. Zbl 1327.65164
Zlotnik, Alexander
7
2015
On \(L^2\)-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations. Zbl 1528.65057
Zlotnik, A. A.; Lomonosov, T. A.
7
2020
On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped. Zbl 1339.65111
Ducomet, Bernard; Zlotnik, Alexander; Romanova, Alla
7
2015
On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations. Zbl 1386.76139
Chetverushkin, B. N.; Zlotnik, A. A.
7
2017
On the quasi-gas dynamic system of equations of state and a heat source. Zbl 1201.76231
Zlotnik, A. A.
6
2010
Linearized stability of equilibrium solutions to the quasi-gasdynamic system of equations. Zbl 1213.35085
Zlotnik, A. A.
6
2010
On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance. Zbl 1330.76103
Gavrilin, V. A.; Zlotnik, A. A.
6
2015
Generalized global solutions of the equations of the one-dimensional motion of a viscous barotropic gas. Zbl 0682.76061
Zlotnik, A. A.; Amosov, A. A.
6
1988
Remark on the stabilization of a viscous barotropic medium with a nonmonotonic equation of state. Zbl 1011.76071
Ducomet, B.; Zlotnik, A. A.
6
2001
Stabilization for 1D radiative and reactive viscous gas flows. Zbl 1042.35045
Ducomet, Bernard; Zlotnik, Alexander
6
2004
Global Lyapunov functionals of the equations for one-dimensional motion of viscous heat-conducting gas. Zbl 1148.76353
Zlotnik, A. A.
6
2002
Stability of numerical methods for solving second-order hyperbolic equations with a small parameter. Zbl 1528.65063
Zlotnik, A. A.; Chetverushkin, B. N.
6
2020
On higher-order compact ADI schemes for the variable coefficient wave equation. Zbl 1510.65217
Zlotnik, Alexander; Čiegis, Raimondas
6
2022
Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis. Zbl 1333.65098
Zlotnik, Alexander; Zlotnik, Ilya
6
2016
Difference schemes of second-order of accuracy for the equations of the one-dimensional motion of a viscous gas. Zbl 0664.76096
Amosov, A. A.; Zlotnik, A. A.
6
1987
\(L^2\)-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations. Zbl 1440.65106
Zlotnik, Alexander; Lomonosov, Timofey
6
2020
Stability of a Numerov type finite-difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis. Zbl 1256.65086
Zlotnik, A. A.; Lapukhina, A. V.
5
2010
A study of a finite-difference method for the one-dimensional viscous heat conductive gas flow equation. I: A priori estimates and stability. Zbl 0825.65063
Amosov, A. A.; Zlotnik, A. A.
5
1987
Entropy balance for the one-dimensional hyperbolic quasi-gasdynamic system of equations. Zbl 1469.76101
Zlotnik, A. A.; Chetverushkin, B. N.
5
2017
A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes. Zbl 1466.65088
Zlotnik, Alexander; Čiegis, Raimondas
5
2021
The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip. Zbl 1315.65072
Ducomet, Bernard; Zlotnik, Alexander; Zlotnik, Ilya
5
2014
On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip. Zbl 1326.65112
Zlotnik, A.; Romanova, A.
5
2015
Family of finite-difference schemes with transparent boundary conditions for the nonstationary Schrödinger equation in a semi-infinite strip. Zbl 1236.65116
Zlotnik, A. A.; Zlotnik, I. A.
5
2011
Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data. Zbl 1086.76590
Amosov, A. A.; Zlotnik, A. A.
5
1998
Properties of generalized solutions of one-dimensional linear parabolic problems with nonsmooth coefficients. Zbl 0912.35072
Amosov, A. A.; Zlotnik, A. A.
5
1997
On global in time properties of the symmetric compressible barotropic Navier-Stokes-Poisson flows in a vacuum. Zbl 1296.76129
Zlotnik, Alexander
5
2008
A “converse” stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation. Zbl 1393.65019
Zlotnik, Alexander; Čiegis, Raimondas
5
2018
Stability of implicit difference schemes for a linearized hyperbolic quasi-gasdynamic system of equations. Zbl 1446.65087
Zlotnik, A. A.; Chetverushkin, B. N.
5
2020
Global properties of quasiaveraged equations of one-dimensional motion of a viscous heat conducting gas. Zbl 0923.76270
Amosov, A. A.; Zlotnik, A. A.
4
1996
The high order method with discrete TBCs for solving the Cauchy problem for the 1D Schrödinger equation. Zbl 1315.65088
Zlotnik, Alexander; Zlotnik, Ilya
4
2015
A difference scheme for the equations of one-dimensional motion of a viscous barotropic gas, its properties and ”global” error estimates. Zbl 0612.65063
Amosov, A. A.; Zlotnik, A. A.
4
1986
Classification of some modifications of the Euler system of equations. Zbl 1327.35325
Zlotnik, A. A.
4
2006
On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier-Stokes equations in polar coordinates. Zbl 1448.65126
Zlotnik, Alexander
4
2018
Semidiscrete method for solving equations of a one-dimensional motion of viscous heat-conductive gas with non-smooth data. Zbl 0911.76078
Amosov, A. A.; Zlotnik, A. A.
4
1997
Global behaviour of 1-D viscous compressible barotropic flows with free boundary and self-gravitation. Zbl 1068.76072
Zlotnik, Alexander
4
2003
On compact 4th order finite-difference schemes for the wave equation. Zbl 1483.65145
Zlotnik, Alexander; Kireeva, Olga
4
2021
On \(L^2\)-dissipativity of linearized explicit finite-difference schemes with a regularization on a non-uniform spatial mesh for the 1D gas dynamics equations. Zbl 1411.65118
Zlotnik, Alexander
4
2019
On quasi-gasdynamic system of equations with general equations of state and its application. Zbl 1237.76157
Zlotnik, Alexander; Gavrilin, Vladimir
4
2011
Lower error estimates for three-layer difference methods of solving the wave equation with data from Hölder spaces. Zbl 0791.65069
Zlotnik, A. A.
3
1992
Estimates of the convergence rate of finite element methods for second order hyperbolic equations. Zbl 0755.65097
Zlotnik, A. A.
3
1991
Some finite-element and finite-difference methods for solving mathematical physics problems with non-smooth data in an \(n\)-dimensional cube. I. Zbl 0816.65063
Zlotnik, A. A.
3
1991
The behavior as \(t\to +\infty\) of solutions to a quasilinear nonstationary problem with free boundaries. Zbl 0834.35104
Zlotnik, A. A.; Nguen Zha Bao
3
1994
Spatial discretization of one-dimensional quasi-gasdynamic systems of equations and the entropy and energy balance equations. Zbl 1357.76079
Zlotnik, A. A.
3
2012
An estimate of the error of quasi-averaging of the equations of motion of a viscous barotropic medium with rapidly oscillating data. Zbl 0923.76263
Amosov, A. A.; Zlotnik, A. A.
3
1996
Stabilization of solutions of a certain quasilinear system of equations with a weakly monotone nonlinearity. Zbl 0976.35054
Zlotnik, A. A.
3
1999
Correctness of the problem of viscous gas burning in the case of nonsmooth data and a semidiscrete method of its solution. Zbl 0948.35119
Zlotnik, A. A.; Puzanov, S. N.
3
1999
Weak solutions to viscous heat-conducting gas 1D-equations with discontinuous data: Global existence, uniqueness, and regularity. Zbl 1007.35081
Zlotnik, Alexander; Amosov, Andrey
3
2002
On a regularization of the magnetic gas dynamics system of equations. Zbl 1264.76117
Ducomet, Bernard; Zlotnik, Alexander
3
2013
Parabolicity of the quasi-gasdynamic system of equations, hyperbolicity of one of its modifications, and stability of small perturbations for them. Zbl 1153.76054
Zlotnik, A. A.; Chetverushkin, B. N.
3
2008
Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations. Zbl 1473.65132
Zlotnik, Alexander; Lomonosov, Timofey
3
2019
Power-rate asymptotic expansion for 1D viscous heat-conducting gas flows. Zbl 1088.76060
Zlotnik, Alexander
3
2006
Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system. Zbl 1530.35087
Zlotnik, A. A.; Chetverushkin, B. N.
3
2023
On construction and properties of compact 4th order finite-difference schemes for the variable coefficient wave equation. Zbl 1518.65096
Zlotnik, Alexander; Čiegis, Raimondas
2
2023
On higher-order compact ADI schemes for the variable coefficient wave equation. Zbl 1510.65217
Zlotnik, Alexander; Čiegis, Raimondas
6
2022
On properties of aggregated regularized systems of equations for a homogeneous multicomponent gas mixture. Zbl 1527.35316
Zlotnik, Alexander; Fedchenko, Anna
2
2022
On the properties of a quasihydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity. Zbl 1506.35181
Zlotnik, A. A.; Fedchenko, A. S.
1
2022
On second-order parabolic and hyperbolic perturbations of a first-order hyperbolic system. Zbl 1504.35414
Zlotnik, A. A.; Chetverushkin, B. N.
1
2022
On a new spatial discretization for a regularized 3D compressible isothermal Navier-Stokes-Cahn-Hilliard system of equations with boundary conditions. Zbl 1475.65063
Balashov, Vladislav; Zlotnik, Alexander
8
2021
A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes. Zbl 1466.65088
Zlotnik, Alexander; Čiegis, Raimondas
5
2021
On compact 4th order finite-difference schemes for the wave equation. Zbl 1483.65145
Zlotnik, Alexander; Kireeva, Olga
4
2021
Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture. Zbl 1504.76065
Zlotnik, A. A.; Fedchenko, A. S.
3
2021
Spectral stability conditions for an explicit three-level finite-difference scheme for a multidimensional transport equation with perturbations. Zbl 1496.65133
Zlotnik, A. A.; Chetverushkin, B. N.
1
2021
\(L^2\)-dissipativity of finite-difference schemes for 1D regularized barotropic gas dynamics equations at small Mach numbers. Zbl 1468.76047
Zlotnik, A. A.; Lomonosov, T. A.
1
2021
An energy dissipative spatial discretization for the regularized compressible Navier-Stokes-Cahn-Hilliard system of equations. Zbl 1476.65159
Balashov, Vladislav; Zlotnik, Alexander
10
2020
An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier-Stokes-Cahn-Hilliard equations. Zbl 1446.65060
Balashov, Vladislav; Zlotnik, Alexander
8
2020
On \(L^2\)-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations. Zbl 1528.65057
Zlotnik, A. A.; Lomonosov, T. A.
7
2020
Stability of numerical methods for solving second-order hyperbolic equations with a small parameter. Zbl 1528.65063
Zlotnik, A. A.; Chetverushkin, B. N.
6
2020
\(L^2\)-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations. Zbl 1440.65106
Zlotnik, Alexander; Lomonosov, Timofey
6
2020
Stability of implicit difference schemes for a linearized hyperbolic quasi-gasdynamic system of equations. Zbl 1446.65087
Zlotnik, A. A.; Chetverushkin, B. N.
5
2020
Fast Fourier solvers for the tensor product high-order FEM for a Poisson type equation. Zbl 1452.65366
Zlotnik, A. A.; Zlotnik, I. A.
1
2020
On enlarged sufficient conditions for \(L^2\)-dissipativity of linearized explicit schemes with regularization for 1D gas dynamics systems of equations. Zbl 1453.65242
Zlotnik, Alexander
1
2020
Conditions for \(L^2\)-dissipativity of linearized explicit difference schemes with regularization for 1D barotropic gas dynamics equations. Zbl 1461.76354
Zlotnik, A. A.; Lomonosov, T. A.
12
2019
Regularized equations for numerical simulation of flows of homogeneous binary mixtures of viscous compressible gases. Zbl 1433.76051
Elizarova, T. G.; Zlotnik, A. A.; Shil’nikov, E. V.
11
2019
Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics. Zbl 1416.76171
Balashov, Vladislav; Savenkov, Evgenii; Zlotnik, Alexander
9
2019
On \(L^2\)-dissipativity of linearized explicit finite-difference schemes with a regularization on a non-uniform spatial mesh for the 1D gas dynamics equations. Zbl 1411.65118
Zlotnik, Alexander
4
2019
Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations. Zbl 1473.65132
Zlotnik, Alexander; Lomonosov, Timofey
3
2019
On a hyperbolic perturbation of a parabolic initial-boundary value problem. Zbl 1524.35281
Chetverushkin, Boris N.; Zlotnik, Alexander A.
12
2018
On conditions for \(L^2\)-dissipativity of linearized explicit QGD finite-difference schemes for one-dimensional gas dynamics equations. Zbl 1408.76396
Zlotnik, A. A.; Lomonosov, T. A.
10
2018
Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients. Zbl 1407.65203
Trautmann, Philip; Vexler, Boris; Zlotnik, Alexander
9
2018
On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations. Zbl 1407.76106
Zlotnik, A.; Lomonosov, T.
8
2018
A “converse” stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation. Zbl 1393.65019
Zlotnik, Alexander; Čiegis, Raimondas
5
2018
On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier-Stokes equations in polar coordinates. Zbl 1448.65126
Zlotnik, Alexander
4
2018
Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data. Zbl 1488.65494
Zlotnik, Alexander; Kireeva, Olga
1
2018
On a finite element method for measure-valued optimal control problems governed by the 1D generalized wave equation. (Sur une méthode d’éléments finis pour résoudre des problèmes de contrôle optimal régis par l’équation d’onde unidimensionnelle généralisée.) Zbl 1401.65112
Vexler, Boris; Zlotnik, Alexander; Trautmann, Philip
1
2018
Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations. Zbl 1457.76129
Zlotnik, A. A.
16
2017
Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface. Zbl 1422.65145
Balashov, Vladislav; Zlotnik, Alexander; Savenkov, Evgeny
16
2017
On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations. Zbl 1386.76139
Chetverushkin, B. N.; Zlotnik, A. A.
7
2017
Entropy balance for the one-dimensional hyperbolic quasi-gasdynamic system of equations. Zbl 1469.76101
Zlotnik, A. A.; Chetverushkin, B. N.
5
2017
A fast direct algorithm for implementing a high-order finite element method on rectangles as applied to boundary value problems for the Poisson equation. Zbl 1371.65123
Zlotnik, A. A.; Zlotnik, I. A.
3
2017
On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force. Zbl 1382.76198
Zlotnik, A. A.
12
2016
Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis. Zbl 1333.65098
Zlotnik, Alexander; Zlotnik, Ilya
6
2016
On a conservative finite-difference method for 1D shallow water flows based on regularized equations. Zbl 1356.76213
Zlotnik, Alexander; Gavrilin, Vladimir
2
2016
On new spatial discretization of the multidimensional quasi-gasdynamic system of equations with nondecreasing total entropy. Zbl 1354.35121
Zlotnik, A. A.
1
2016
The Numerov-Crank-Nicolson scheme on a non-uniform mesh for the time-dependent Schrödinger equation on the half-axis. Zbl 1327.65164
Zlotnik, Alexander
7
2015
On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped. Zbl 1339.65111
Ducomet, Bernard; Zlotnik, Alexander; Romanova, Alla
7
2015
On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance. Zbl 1330.76103
Gavrilin, V. A.; Zlotnik, A. A.
6
2015
On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip. Zbl 1326.65112
Zlotnik, A.; Romanova, A.
5
2015
The high order method with discrete TBCs for solving the Cauchy problem for the 1D Schrödinger equation. Zbl 1315.65088
Zlotnik, Alexander; Zlotnik, Ilya
4
2015
Error estimates of the Crank-Nicolson-polylinear FEM with the discrete TBC for the generalized Schrödinger equation in an unbounded parallelepiped. Zbl 1359.65174
Zlotnik, Alexander
2
2015
Splitting in potential finite-difference schemes with discrete transparent boundary conditions for the time-dependent Schrödinger equation. Zbl 1328.65188
Zlotnik, Alexander; Ducomet, Bernard; Zlotnik, Ilya; Romanova, Alla
1
2015
On quasi-gasdynamic and quasi-hydrodynamic equations for binary gas mixtures. Zbl 1315.76028
Elizarova, T. G.; Zlotnik, A. A.; Chetverushkin, B. N.
11
2014
The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip. Zbl 1315.65072
Ducomet, Bernard; Zlotnik, Alexander; Zlotnik, Ilya
5
2014
On a regularization of the magnetic gas dynamics system of equations. Zbl 1264.76117
Ducomet, Bernard; Zlotnik, Alexander
3
2013
On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force. Zbl 1289.76068
Zlotnik, A. A.
17
2012
Spatial discretization of the one-dimensional quasi-gasdynamic system of equations and the entropy balance equation. Zbl 1274.35301
Zlotnik, A. A.
11
2012
Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation. Zbl 1267.65144
Zlotnik, Alexander; Zlotnik, Ilya
10
2012
The space discretization of the one-dimensional barotropic quasi-gas dynamic system of equations and the energy balance equation. Zbl 1289.76074
Zlotnik, A. A.
8
2012
Spatial discretization of one-dimensional quasi-gasdynamic systems of equations and the entropy and energy balance equations. Zbl 1357.76079
Zlotnik, A. A.
3
2012
Finite element method with discrete transparent boundary conditions for the one-dimensional nonstationary Schrödinger equation. Zbl 1262.65135
Zlotnik, A. A.; Zlotnik, I. A.
1
2012
Family of finite-difference schemes with transparent boundary conditions for the nonstationary Schrödinger equation in a semi-infinite strip. Zbl 1236.65116
Zlotnik, A. A.; Zlotnik, I. A.
5
2011
On quasi-gasdynamic system of equations with general equations of state and its application. Zbl 1237.76157
Zlotnik, Alexander; Gavrilin, Vladimir
4
2011
Energy equalities and estimates for barotropic quasi-gasdynamic and quasi-hydrodynamic systems of equations. Zbl 1224.35356
Zlotnik, A. A.
18
2010
Quasi-gasdynamic system of equations with general equations of state. Zbl 1387.35510
Zlotnik, A. A.
12
2010
On the quasi-gas dynamic system of equations of state and a heat source. Zbl 1201.76231
Zlotnik, A. A.
6
2010
Linearized stability of equilibrium solutions to the quasi-gasdynamic system of equations. Zbl 1213.35085
Zlotnik, A. A.
6
2010
Stability of a Numerov type finite-difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis. Zbl 1256.65086
Zlotnik, A. A.; Lapukhina, A. V.
5
2010
On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation. Zbl 1195.65106
Ducomet, Bernard; Zlotnik, Alexander; Zlotnik, Ilya
12
2009
On one version of a semidiscrete Galerkin method for PDE problems involving a generalized 2D Hamiltonian operator. Zbl 1188.65129
Zlotnik, Alexander; Ducomet, Bernard; Goutte, Heloise; Berger, Jean-Francois
1
2009
Error bounds for finite element methods with generalized cubic splines for a 4-th order ordinary differential equation with nonsmooth data. Zbl 1188.65109
Zlotnik, A.; Kireeva, O.
1
2009
Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them. Zbl 1201.76232
Zlotnik, A. A.; Chetverushkin, B. N.
33
2008
Parabolicity of a quasihydrodynamic system of equations and the stability of its small perturbations. Zbl 1160.35326
Zlotnik, A. A.
15
2008
On global in time properties of the symmetric compressible barotropic Navier-Stokes-Poisson flows in a vacuum. Zbl 1296.76129
Zlotnik, Alexander
5
2008
Parabolicity of the quasi-gasdynamic system of equations, hyperbolicity of one of its modifications, and stability of small perturbations for them. Zbl 1153.76054
Zlotnik, A. A.; Chetverushkin, B. N.
3
2008
On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. II. Zbl 1141.65069
Ducomet, B.; Zlotnik, A.
8
2007
On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. I. Zbl 1119.65085
Ducomet, B.; Zlotnik, A.
11
2006
Classification of some modifications of the Euler system of equations. Zbl 1327.35325
Zlotnik, A. A.
4
2006
Power-rate asymptotic expansion for 1D viscous heat-conducting gas flows. Zbl 1088.76060
Zlotnik, Alexander
3
2006
Stability criterion for small perturbations for a quasi-gasdynamic system of equations. Zbl 1210.76145
Zlotnik, A. A.; Zlotnik, I. A.
1
2006
Sharp error bounds for a symmetrized locally 1D method for solving the 2D heat equation. Zbl 1094.65094
Zlotnik, Alexander; Ilyicheva, Svetlana
1
2006
Lyapunov functional method for 1D radiative and reactive viscous gas dynamics. Zbl 1070.76044
Ducomet, Bernard; Zlotnik, Alexander
51
2005
On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics. Zbl 1083.35109
Ducomet, Bernard; Zlotnik, Alexander
38
2005
Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system. Zbl 1125.35071
Ducomet, B.; Zlotnik, A.
15
2005
Stabilization rate and stability for viscous compressible barotropic symmetric flows with free boundary for a general mass force. Zbl 1151.35432
Zlotnik, A. A.; Ducomet, B.
11
2005
Viscous compressible barotropic symmetric flows with free boundary under general mass force I: Uniform-in-time bounds and stabilization. Zbl 1068.35102
Ducomet, Bernard; Zlotnik, Alexander
10
2005
The problem of symmetric equilibrium in compressible barotropic fluids with a free surface for a general body force. Zbl 1272.35163
Zlotnik, A. A.; Ducomet, B.
2
2005
Lyapunov functionals of symmetric flows of a viscous compressible barotropic fluid with a free surface for a general body force. Zbl 1272.35164
Zlotnik, A. A.; Ducomet, B.
1
2005
Stabilization of one-dimensional flows of radiative and reactive viscous gas for a general rate of reaction. Zbl 1140.35554
Zlotnik, A. A.; Ducomet, B.
1
2005
Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data. Zbl 1072.35082
Jiang, Song; Zlotnik, Alexander
16
2004
Weak solutions to the equations of motion of viscous compressible reacting binary mixtures: uniqueness and Lipschitz-continuous dependence on data. Zbl 1122.35118
Zlotnik, A. A.
9
2004
Stabilization for 1D radiative and reactive viscous gas flows. Zbl 1042.35045
Ducomet, Bernard; Zlotnik, Alexander
6
2004
Global properties of solutions to 1D-viscous compressible barotropic fluid equations with density dependent viscosity. Zbl 1040.35064
Straškraba, Ivan; Zlotnik, Alexander
27
2003
Global behavior of 1d-viscous compressible barotropic fluid with a free boundary and large data. Zbl 1042.76050
Straškraba, Ivan; Zlotnik, Alexander
13
2003
Stabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state. Zbl 1160.35491
Ducomet, Bernard; Zlotnik, Alexander
8
2003
Global behaviour of 1-D viscous compressible barotropic flows with free boundary and self-gravitation. Zbl 1068.76072
Zlotnik, Alexander
4
2003
Stress and heat flux stabilization for viscous compressible medium equations with a nonmonotone state function. Zbl 1043.35107
Zlotnik, A. A.
1
2003
On a decay rate for 1D-viscous compressible barotropic fluid equations. Zbl 1038.35065
Straškraba, Ivan; Zlotnik, Alexander
14
2002
Stabilization for viscous compressible heat-conducting media equations with nonmonotone state functions. Zbl 1078.35524
Ducomet, Bernard; Zlotnik, Alexander
10
2002
Global Lyapunov functionals of the equations for one-dimensional motion of viscous heat-conducting gas. Zbl 1148.76353
Zlotnik, A. A.
6
2002
Weak solutions to viscous heat-conducting gas 1D-equations with discontinuous data: Global existence, uniqueness, and regularity. Zbl 1007.35081
Zlotnik, Alexander; Amosov, Andrey
3
2002
On the stabilization of a viscous barotropic self-gravitating medium with a nonmonotone equation of state. Zbl 1020.76045
Ducomet, B.; Zlotnik, A. A.
2
2002
On superconvergence of a gradient for finite element methods for an elliptic equation with the nonsmooth right-hand side. Zbl 1015.65059
Zlotnik, A.
2
2002
...and 57 more Documents
all top 5

Cited by 423 Authors

90 Zlotnik, Alexander A.
23 Chetverushkin, Boris Nikolaevich
18 Ducomet, Bernard
13 Xin, Zhouping
12 Elizarova, Tat’yana Gennad’evna
12 Zhu, Changjiang
11 Zhang, Jianwen
9 Amosov, Andreĭ Avenirovich
9 Čiegis, Raimondas
9 Li, Jinkai
9 Shang, Zhaoyang
8 Balashov, Vladislav
8 Lomonosov, T. A.
8 Qin, Yuming
8 Zhang, Ting
7 Guo, Zhenhua
7 Li, Jing
7 Liao, Yongkai
6 Fang, Daoyuan
6 Huang, Bin
6 Huang, Lan
6 Kriksin, Yu. A.
6 Li, Hailiang
6 Liu, Yang
6 Nečasová, Šárka
6 Shi, Xiaoding
6 Tishkin, Vladimir Fëdorovich
5 Balashov, V. A.
5 Hong, GuangYi
5 Jiu, Quansen
5 Li, Zilai
5 Lutsky, A. E.
5 Peng, Lishuang
5 Prokudin, Dmitriĭ Alekseevich
5 Radziunas, Mindaugas
5 Sun, Ying
5 Wen, Huanyao
5 Zhang, Mingyu
5 Zhao, Junning
5 Zhong, Xin
4 Bresch, Didier
4 Duan, Qin
4 Fan, Jishan
4 Hou, Xiaofeng
4 Li, Yang
4 Li, Yong
4 Mamontov, Aleksandr Evgen’evich
4 Peng, Hongyun
4 Podryga, Viktoriia O.
4 Polyakov, Sergey V.
4 Savenkov, E. B.
4 Shilnikov, Eugene V.
4 Si, Xin
4 Straškraba, Ivan
4 Wang, Yi
4 Yao, Zhengan
4 Ye, Yulin
4 Zatorska, Ewelina
4 Zhang, Lan
4 Zhang, Peixin
4 Zhao, Huijiang
4 Zlotnik, I. A.
3 Bragin, Michael D.
3 Bulatov, O. V.
3 Chen, Yazhou
3 Dou, Changsheng
3 Evje, Steinar
3 Fedchenko, A. S.
3 Hu, Guili
3 Huang, Bingkang
3 Huang, Bingyuan
3 Huang, Xiangdi
3 Jiang, Peng
3 Jiang, Song
3 Liu, Hao
3 Lomonosov, Timofey
3 Mahmood, Tariq
3 Peng, Yi
3 Romanova, Alla
3 Saveliev, Valeri I.
3 Savenkov, Evgeny
3 Steinbach, Olaf
3 Sun, Yongzhong
3 Tan, Zhong
3 Tani, Atusi
3 Trautmann, Philip
3 Umehara, Morimichi
3 Vexler, Boris
3 Wan, Ling
3 Wang, Taige
3 Wang, Tao
3 Wang, Wenjun
3 Yang, Jing
3 Yu, Haibo
3 Zank, Marco
3 Zhang, Jianlin
3 Zhao, Xiaokui
3 Zi, Ruizhao
2 Abd Hamid, Nur Nadiah
2 Bugajev, Andrej
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Cited in 108 Serials

33 Journal of Differential Equations
27 Mathematical Methods in the Applied Sciences
25 Doklady Mathematics
18 Journal of Mathematical Analysis and Applications
18 Computational Mathematics and Mathematical Physics
15 Journal of Mathematical Physics
14 ZAMP. Zeitschrift für angewandte Mathematik und Physik
14 Journal of Mathematical Fluid Mechanics
13 Matematicheskoe Modelirovanie
12 Mathematical Notes
10 Differential Equations
10 Nonlinear Analysis. Real World Applications
9 Archive for Rational Mechanics and Analysis
9 Applied Mathematics Letters
9 Journal of Mathematical Sciences (New York)
9 Mathematical Modelling and Analysis
8 Acta Mathematicae Applicatae Sinica. English Series
8 Science China. Mathematics
7 Communications in Mathematical Physics
7 Journal of Computational Physics
7 Russian Journal of Numerical Analysis and Mathematical Modelling
6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
6 Lobachevskii Journal of Mathematics
6 Acta Mathematica Scientia. Series B. (English Edition)
5 Nonlinearity
5 Applied Numerical Mathematics
5 SIAM Journal on Mathematical Analysis
4 Computers & Mathematics with Applications
4 Lithuanian Mathematical Journal
4 Discrete and Continuous Dynamical Systems. Series B
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Boundary Value Problems
3 Applicable Analysis
3 Computer Physics Communications
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Journal of Computational and Applied Mathematics
3 Acta Applicandae Mathematicae
3 Journal of Scientific Computing
3 Journal de Mathématiques Pures et Appliquées. Neuvième Série
3 Discrete and Continuous Dynamical Systems
3 Abstract and Applied Analysis
3 Journal of Inequalities and Applications
3 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki
3 Advances in Difference Equations
3 Sibirskie Èlektronnye Matematicheskie Izvestiya
3 Kinetic and Related Models
3 Mathematical Control and Related Fields
2 Communications on Pure and Applied Mathematics
2 Applied Mathematics and Computation
2 Numerical Functional Analysis and Optimization
2 Siberian Mathematical Journal
2 Physica D
2 Acta Mathematica Sinica. English Series
2 Communications on Pure and Applied Analysis
2 Analysis and Applications (Singapore)
2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche
2 Journal of Function Spaces
1 Computers and Fluids
1 International Journal of Engineering Science
1 Journal of Applied Mathematics and Mechanics
1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1 Mathematics of Computation
1 Advances in Mathematics
1 Applied Mathematics and Optimization
1 Journal of Functional Analysis
1 Mathematische Annalen
1 Mathematics and Computers in Simulation
1 Mathematische Nachrichten
1 Osaka Journal of Mathematics
1 Proceedings of the Japan Academy. Series A
1 Quarterly of Applied Mathematics
1 SIAM Journal on Numerical Analysis
1 Studies in Applied Mathematics
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Computational Mathematics and Modeling
1 The Journal of Geometric Analysis
1 Applications of Mathematics
1 Communications in Partial Differential Equations
1 Pattern Recognition
1 Journal of Dynamics and Differential Equations
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Russian Mathematics
1 Applied Mathematics. Series B (English Edition)
1 Calculus of Variations and Partial Differential Equations
1 Russian Journal of Mathematical Physics
1 Bulletin des Sciences Mathématiques
1 Monte Carlo Methods and Applications
1 Sbornik: Mathematics
1 Mathematical Problems in Engineering
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Mathematical Physics, Analysis and Geometry
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Journal of Dynamical and Control Systems
1 Communications in Contemporary Mathematics
1 Journal of Evolution Equations
1 Computational Methods in Applied Mathematics
1 Doklady Natsional’noĭ Akademii Nauk Belarusi
1 Journal of Hyperbolic Differential Equations
...and 8 more Serials

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