Zlotnik Alexander Anatol'evich

Publications in Math-Net.Ru

1. Application of regularized equations for dynamics of heterogeneous binary mixtures to modeling water-vapor phase transitions
   
   Mat. Model., 37:1 (2025),  151–170
2. Derivation of lower error bounds for the bilinear element method with a weight for the one-dimensional wave equation
   
   Zh. Vychisl. Mat. Mat. Fiz., 65:2 (2025),  140–149
3. On properties of a semi-explicit vector compact scheme for the acoustic wave equation
   
   Russian Journal of Cybernetics, 5:3 (2024),  6–12
4. Regularized equations for dynamics of the heterogeneous binary mixtures of the Noble-Abel stiffened-gases and their application
   
   Dokl. RAN. Math. Inf. Proc. Upr., 514:1 (2023),  26–33
5. Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system
   
   Mat. Sb., 214:4 (2023),  3–37
6. On the construction of regularized equations of motion for a mixture of viscous incompressible fluids
   
   Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022),  89–94
7. On second-order parabolic and hyperbolic perturbations of a first-order hyperbolic system
   
   Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022),  9–15
8. Conditions for dissipativity of an explicit finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations
   
   Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022),  30–36
9. On $L^2$-dissipativity of a linearized scheme on staggered meshes with a regularization for 1D barotropic gas dynamics equations
   
   Zh. Vychisl. Mat. Mat. Fiz., 62:12 (2022),  1981–2001
10. Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture
    
    Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021),  31–37
11. Properties of the aggregated quasi-hydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity
    
    Keldysh Institute preprints, 2021, 077, 26 pp.
12. On $L^2$-dissipativity of a linearized difference scheme on staggered meshes with a quasi-hydrodynamic regularization for $\mathrm{1D}$ barotropic gas dynamics equations
    
    Keldysh Institute preprints, 2021, 072, 27 pp.
13. $L^2$-dissipativity of finite-difference schemes for $\mathrm{1D}$ regularized barotropic gas dynamics equations at small Mach numbers
    
    Mat. Model., 33:5 (2021),  16–34
14. On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations
    
    Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020),  31–37
15. Stability of numerical methods for solving second-order hyperbolic equations with a small parameter
    
    Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020),  35–41
16. Fast Fourier solvers for the tensor product high-order fem for a Poisson type equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 60:2 (2020),  234–252
17. Regularized equations for numerical simulation of flows of homogeneous binary mixtures of viscous compressible gases
    
    Zh. Vychisl. Mat. Mat. Fiz., 59:11 (2019),  1899–1914
18. Conditions for $L^2$-dissipativity of linearized explicit difference schemes with regularization for $\mathrm{1D}$ barotropic gas dynamics equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 59:3 (2019),  481–493
19. Numerical algorithm for simulation of three-dimensional two-phase flows with surface effects within domains with voxel geometry
    
    Keldysh Institute preprints, 2017, 091, 28 pp.
20. On two-dimensional numerical QGD-modelling of spiral-vortex structures in accretion gas disks
    
    Keldysh Institute preprints, 2017, 001, 30 pp.
21. Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017),  710–729
22. A study of the barotropic quasi-hydrodynamic model for the two-phase mixture involving surface effects
    
    Keldysh Institute preprints, 2016, 089, 25 pp.
23. On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force
    
    Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016),  301–317
24. On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance
    
    Zh. Vychisl. Mat. Mat. Fiz., 55:2 (2015),  267–284
25. The space discretization of the one-dimensional barotropic quasi-gas dynamic system of equations and the energy balance equation
    
    Mat. Model., 24:10 (2012),  51–64
26. On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force
    
    Mat. Model., 24:4 (2012),  65–79
27. Spatial discretization of the one-dimensional quasi-gasdynamic system of equations and the entropy balance equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 52:7 (2012),  1304–1316
28. Modeling of one-dimensional shallow water flows based on regularized equations
    
    Keldysh Institute preprints, 2011, 033, 36 pp.
29. On the quasi-gasdynamic system of equations with general equations of state and a heat source
    
    Mat. Model., 22:7 (2010),  53–64
30. On stability of small perturbations for a modified two-dimensional quasi-gasdynamic model of traffic flows
    
    Mat. Model., 22:4 (2010),  110–117
31. Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010),  325–337
32. Some properties of the equations governing a two-dimensional quasi-gasdynamic model of traffic flows
    
    Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009),  373–381
33. Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations
    
    Mat. Zametki, 83:5 (2008),  667–682
34. Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them
    
    Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008),  445–472
35. On the stability of the $\sigma$-scheme with transparent boundary conditions for parabolic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007),  671–692
36. Stability criterion for small perturbations for a quasi-gasdynamic system of equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:2 (2006),  262–269
37. Stabilization rate and stability for viscous compressible barotropic symmetric flows with free boundary for a general mass force
    
    Mat. Sb., 196:12 (2005),  33–84
38. Weak Solutions to the Equations of Motion of Viscous Compressible Reacting Binary Mixtures: Uniqueness and Lipschitz-Continuous Dependence on Data
    
    Mat. Zametki, 75:2 (2004),  307–310
39. On a variable weight difference scheme for the equations of the one-dimension motion of a viscous compressible barotropic fluid
    
    Zh. Vychisl. Mat. Mat. Fiz., 44:6 (2004),  1079–1092
40. Well-Definedness of the Cauchy Problem for the One-Dimensional Equations of Viscous Heat Conducting Gas with Initial Data from Lebesgue Spaces
    
    Mat. Zametki, 73:5 (2003),  779–783
41. Substantiation of two-scale homogenization of one-dimensional nonlinear thermoviscoelasticity equations with nonsmooth data
    
    Zh. Vychisl. Mat. Mat. Fiz., 41:11 (2001),  1713–1733
42. Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations
    
    Differ. Uravn., 36:5 (2000),  634–646
43. Stabilization of solutions of a quasilinear system of equations with a nonstrictly monotone nonlinearity
    
    Differ. Uravn., 35:10 (1999),  1403–1407
44. On some properties of the alternating triangular vector method for the heat equation
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 7,  3–11
45. A semidiscrete method for solving equations of the one-dimensional motion of a viscous heat-conducting gas with nonsmooth data. Regularity of solutions
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 5,  12–25
46. The well-posedness of the combustion problem for a viscous gas in the case of nonsmooth data, and a semidiscrete method for its solution
    
    Mat. Zametki, 65:6 (1999),  944–948
47. A finite difference scheme for quasi-averaged equations of one-dimensional viscous heat-conducting gas flow with nonsmooth data
    
    Zh. Vychisl. Mat. Mat. Fiz., 39:4 (1999),  592–611
48. Sharp error estimates of vector splitting methods for the heat equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 39:3 (1999),  472–491
49. Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases
    
    Mat. Zametki, 63:6 (1998),  835–846
50. On Nishida's problem
    
    Zh. Vychisl. Mat. Mat. Fiz., 38:8 (1998),  1279–1286
51. Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data
    
    Zh. Vychisl. Mat. Mat. Fiz., 38:7 (1998),  1204–1219
52. Justification of the quasi-averaging of equations of the one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating properties
    
    Dokl. Akad. Nauk, 354:4 (1997),  439–442
53. On properties of generalized solutions of one-dimensional linear parabolic problems with nonsmooth coefficients
    
    Differ. Uravn., 33:1 (1997),  83–95
54. Exact estimates for the error gradient of locally one-dimensional methods for multidimensional equation of heat conduction
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1997, no. 4,  51–65
55. A semidiscrete method for solving equations of the one-dimensional motion of a non-homogeneous viscous heat-conducting gas with nonsmooth data
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1997, no. 4,  3–19
56. On the stability of generalized solutions of equations of one-dimensional motion of a viscous heat-conducting gas
    
    Sibirsk. Mat. Zh., 38:4 (1997),  767–789
57. Properties “in the large” of quasi-averaged equations of the one-dimensional motion of a viscous heat-conducting gas
    
    Dokl. Akad. Nauk, 346:2 (1996),  151–154
58. Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation
    
    Mat. Zametki, 60:2 (1996),  185–197
59. Finite-element methods for the problem of dynamic vibrations of an inhomogeneous bar with nonsmooth data
    
    Mat. Zametki, 60:1 (1996),  138–143
60. Exact analysis of the error of locally one-dimensional methods for the heat equation with a right-hand side in $L_2$
    
    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 6,  40–43
61. An estimate of the error of quasi-averaging of the equations of motion of a viscous barotropic medium with rapidly oscillating data
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:10 (1996),  111–128
62. On quasi-averaged equations of the one-dimensional motion of a viscous barotropic medium with rapidly oscillating data
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:2 (1996),  87–110
63. Justification of quasi-averaged equations of the one-dimensional motion of a viscous barotropic medium with rapidly oscillating properties
    
    Dokl. Akad. Nauk, 342:3 (1995),  295–299
64. Uniqueness and stability of generalized solutions of quasi-averaged equations of the one-dimensional motion of a viscous barotropic medium
    
    Differ. Uravn., 31:7 (1995),  1123–1131
65. On the error of some projection-grid methods for a fourth-order ordinary differential equation with nonsmooth data
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 4,  49–61
66. Uniform estimates and stabilization of solutions to equations of one-dimensional motion of a multicomponent barotropic mixture
    
    Mat. Zametki, 58:2 (1995),  307–312
67. On the behavior as $t\to+\infty$ of solutions of a quasilinear nonstationary problem with free boundaries
    
    Differ. Uravn., 30:6 (1994),  1080–1082
68. Solvability “in the large” of a class of quasilinear systems of equations of composite type with nonsmooth data
    
    Differ. Uravn., 30:4 (1994),  596–609
69. On estimates for the solutions of difference equations of the one-dimensional motion of a viscous barotropic gas
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 9,  49–59
70. Uniqueness and stability of generalized solutions for a class of quasilinear systems of composite type equations
    
    Mat. Zametki, 55:6 (1994),  13–31
71. Properties and asymptotic behavior of solutions of some problems of one-dimensional motion of a viscous barotropic gas
    
    Mat. Zametki, 55:5 (1994),  51–68
72. Solvability “in the large” of a system of equations of the one-dimensional motion of an inhomogeneous viscous heat-conducting gas
    
    Mat. Zametki, 52:2 (1992),  3–16
73. On one family of integral functionals
    
    Mat. Zametki, 52:1 (1992),  144–146
74. Two-layer projection-difference method with a splitting operator for the wave equation
    
    Mat. Zametki, 51:4 (1992),  23–35
75. Lower error estimates for three-layer difference methods of solving the wave equation with data from holder spaces
    
    Mat. Zametki, 51:3 (1992),  140–142
76. Equations of one-dimensional motion of a viscous barotropic gas in the presence of mass force
    
    Sibirsk. Mat. Zh., 33:5 (1992),  62–79
77. Properties of a projection-grid method with a quasidecoupled operator for second-order hyperbolic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 32:4 (1992),  542–549
78. A difference scheme on a non-uniform mesh for the equations of one-dimensional magnetic gas dynamics
    
    Zh. Vychisl. Mat. Mat. Fiz., 29:4 (1989),  521–534
79. Generalized solutions “in the large” of the equations of the one-dimensional motion of a viscous heat-conducting gas
    
    Dokl. Akad. Nauk SSSR, 301:1 (1988),  11–15
80. Generalized solutions “in the large” of equations of the one-dimensional motion of a viscous barotropic gas
    
    Dokl. Akad. Nauk SSSR, 299:6 (1988),  1303–1307
81. A family of difference schemes for equations of one-dimensional magnetogasdynamics: properties and error estimates “in the large”
    
    Dokl. Akad. Nauk SSSR, 299:6 (1988),  1295–1299
82. Difference schemes of second-order of accuracy for the equations of the one-dimensional motion of a viscous gas
    
    Zh. Vychisl. Mat. Mat. Fiz., 27:7 (1987),  1032–1049
83. A difference scheme for equations of one-dimensional motion of a viscous barotropic gas, its properties and estimates of the error “in the large”
    
    Dokl. Akad. Nauk SSSR, 288:2 (1986),  270–275
84. A difference scheme for equations of motion of a viscous heat conducting gas, its properties and error estimates “in the large”
    
    Dokl. Akad. Nauk SSSR, 284:2 (1985),  265–269
85. Sharp error estimates of some two-level methods of solving the three-dimensional heat equation
    
    Mat. Sb. (N.S.), 128(170):4(12) (1985),  530–544
86. Coefficient stability of systems of ordinary differential equations
    
    Differ. Uravn., 20:2 (1984),  220–229
87. Sharp estimates for error and optimality of two-layered efficient methods of solution of the heat equation
    
    Dokl. Akad. Nauk SSSR, 272:6 (1983),  1306–1311
88. The rate of convergence in $W^1_{2,h}$ of the variational-difference method for elliptic equations
    
    Dokl. Akad. Nauk SSSR, 271:4 (1983),  784–788
89. A set of routines for the solution of problems of nonlinear optics
    
    Zh. Vychisl. Mat. Mat. Fiz., 22:3 (1982),  756–758
90. On the rate of convergence of the projection-difference scheme with a splitting operator for parabolic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 20:2 (1980),  422–432
91. A projection-difference scheme for the vibrating-string equation
    
    Dokl. Akad. Nauk SSSR, 245:2 (1979),  292–295
92. Coefficient stability of differential equations and averaging of equations with random coefficients
    
    Dokl. Akad. Nauk SSSR, 242:4 (1978),  745–748
93. An estimate of the rate of convergence in $L_2$ of projection-difference schemes for parabolic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 18:6 (1978),  1454–1465
94. Description of a program set for solution of the light-wave propagation equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 17:4 (1977),  1074–1076


95. Correction: “Sharp estimates for error and optimality of two-layered efficient methods of solution of the heat equation”
    
    Dokl. Akad. Nauk SSSR, 276:4 (1984),  776