Publications in Math-Net.Ru |
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2019 |
1. |
T. G. Elizarova, A. A. Zlotnik, E. V. Shilnikov, “Регуляризованные уравнения для численного моделирования течений гомогенных бинарных смесей вязких сжимаемых газов”, Zh. Vychisl. Mat. Mat. Fiz., 59:11 (2019), 1899–1914 |
2. |
A. A. Zlotnik, T. A. Lomonosov, “Условия $L^2$-диссипативности линеаризованных явных разностных схем с регуляризацией для уравнений $\mathrm{1D}$ баротропной газовой динамики”, Zh. Vychisl. Mat. Mat. Fiz., 59:3 (2019), 481–493 |
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2017 |
3. |
V. A. Balashov, A. A. Zlotnik, E. B. Savenkov, “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. |
4. |
T. G. Elizarova, A. A. Zlotnik, M. A. Istomina, “On two-dimensional numerical QGD-modelling of spiral-vortex structures in accretion gas disks”, Keldysh Institute preprints, 2017, 001, 30 pp. |
5. |
A. A. Zlotnik, “Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 710–729 ; Comput. Math. Math. Phys., 57:4 (2017), 706–725 |
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2016 |
6. |
V. A. Balashov, A. A. Zlotnik, E. B. Savenkov, “A study of the barotropic quasi-hydrodynamic model for the two-phase mixture involving surface effects”, Keldysh Institute preprints, 2016, 089, 25 pp. |
7. |
A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 56:2 (2016), 303–319 |
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2015 |
8. |
V. A. Gavrilin, A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 55:2 (2015), 264–281 |
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2012 |
9. |
A. A. Zlotnik, “The space discretization of the one-dimensional barotropic quasi-gas dynamic system of equations and the energy balance equation”, Matem. Mod., 24:10 (2012), 51–64 |
10. |
A. A. Zlotnik, “On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force”, Matem. Mod., 24:4 (2012), 65–79 |
11. |
A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 52:7 (2012), 1060–1071 |
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2011 |
12. |
T. G. Elizarova, A. A. Zlotnik, O. V. Nikitina, “Modeling of one-dimensional shallow water flows based on regularized equations”, Keldysh Institute preprints, 2011, 033, 36 pp. |
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2010 |
13. |
A. A. Zlotnik, “On the quasi-gasdynamic system of equations with general equations of state and a heat source”, Matem. Mod., 22:7 (2010), 53–64 |
14. |
A. A. Zlotnik, “On stability of small perturbations for a modified two-dimensional quasi-gasdynamic model of traffic flows”, Matem. Mod., 22:4 (2010), 110–117 ; Math. Models Comput. Simul., 2:6 (2010), 776–781 |
15. |
A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 50:2 (2010), 310–321 |
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2009 |
16. |
A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 49:2 (2009), 363–372 |
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2008 |
17. |
A. A. Zlotnik, “Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations”, Mat. Zametki, 83:5 (2008), 667–682 ; Math. Notes, 83:5 (2008), 610–623 |
18. |
A. A. Zlotnik, B. N. Chetverushkin, “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 ; Comput. Math. Math. Phys., 48:3 (2008), 420–446 |
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2007 |
19. |
A. A. Zlotnik, “On the stability of the $\sigma$-scheme with transparent boundary conditions for parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 671–692 ; Comput. Math. Math. Phys., 47:4 (2007), 644–663 |
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2006 |
20. |
A. A. Zlotnik, I. A. Zlotnik, “Stability criterion for small perturbations for a quasi-gasdynamic system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 46:2 (2006), 262–269 ; Comput. Math. Math. Phys., 46:2 (2006), 251–257 |
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2005 |
21. |
A. A. Zlotnik, B. Ducomet, “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 ; Sb. Math., 196:12 (2005), 1745–1799 |
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2004 |
22. |
A. A. Zlotnik, “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 ; Math. Notes, 75:2 (2004), 278–283 |
23. |
V. V. Gileva, A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 44:6 (2004), 1024–1037 |
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2003 |
24. |
A. A. Zlotnik, Sun Jiang, “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 ; Math. Notes, 73:5 (2003), 730–735 |
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2001 |
25. |
A. A. Amosov, A. A. Zlotnik, “Substantiation of two-scale homogenization of one-dimensional nonlinear thermoviscoelasticity equations with nonsmooth data”, Zh. Vychisl. Mat. Mat. Fiz., 41:11 (2001), 1713–1733 ; Comput. Math. Math. Phys., 41:11 (2001), 1630–1650 |
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2000 |
26. |
A. A. Zlotnik, “Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations”, Differ. Uravn., 36:5 (2000), 634–646 ; Differ. Equ., 36:5 (2000), 701–716 |
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1999 |
27. |
A. A. Zlotnik, “Stabilization of solutions of a quasilinear system of equations with a nonstrictly monotone nonlinearity”, Differ. Uravn., 35:10 (1999), 1403–1407 ; Differ. Equ., 35:10 (1999), 1423–1428 |
28. |
S. B. Zaitseva, A. A. Zlotnik, “On some properties of the alternating triangular vector method for the heat equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, 7, 3–11 ; Russian Math. (Iz. VUZ), 43:7 (1999), 1–9 |
29. |
A. A. Amosov, A. A. Zlotnik, “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, 5, 12–25 ; Russian Math. (Iz. VUZ), 43:5 (1999), 10–23 |
30. |
A. A. Zlotnik, S. N. Puzanov, “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 ; Math. Notes, 65:6 (1999), 793–797 |
31. |
A. A. Amosov, A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 39:4 (1999), 564–583 |
32. |
S. B. Zaitseva, A. A. Zlotnik, “Sharp error estimates of vector splitting methods for the heat equation”, Zh. Vychisl. Mat. Mat. Fiz., 39:3 (1999), 472–491 ; Comput. Math. Math. Phys., 39:3 (1999), 448–467 |
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1998 |
33. |
A. A. Zlotnik, A. A. Amosov, “Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases”, Mat. Zametki, 63:6 (1998), 835–846 ; Math. Notes, 63:6 (1998), 736–746 |
34. |
A. A. Zlotnik, “On Nishida's problem”, Zh. Vychisl. Mat. Mat. Fiz., 38:8 (1998), 1279–1286 ; Comput. Math. Math. Phys., 38:8 (1998), 1225–1232 |
35. |
A. A. Amosov, A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 38:7 (1998), 1152–1167 |
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1997 |
36. |
A. A. Amosov, A. A. Zlotnik, “On properties of generalized solutions of one-dimensional linear parabolic problems with nonsmooth coefficients”, Differ. Uravn., 33:1 (1997), 83–95 ; Differ. Equ., 33:1 (1997), 83–96 |
37. |
S. B. Zaitseva, A. A. Zlotnik, “Exact estimates for the error gradient of locally one-dimensional methods for multidimensional equation of heat conduction”, Izv. Vyssh. Uchebn. Zaved. Mat., 1997, 4, 51–65 ; Russian Math. (Iz. VUZ), 41:4 (1997), 49–63 |
38. |
A. A. Amosov, A. A. Zlotnik, “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, 4, 3–19 ; Russian Math. (Iz. VUZ), 41:4 (1997), 1–17 |
39. |
A. A. Zlotnik, A. A. Amosov, “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 ; Siberian Math. J., 38:4 (1997), 663–684 |
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1996 |
40. |
S. B. Zaitseva, A. A. Zlotnik, “Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation”, Mat. Zametki, 60:2 (1996), 185–197 ; Math. Notes, 60:2 (1996), 137–146 |
41. |
A. A. Zlotnik, O. I. Kireeva, “Finite-element methods for the problem of dynamic vibrations of an inhomogeneous bar with nonsmooth data”, Mat. Zametki, 60:1 (1996), 138–143 ; Math. Notes, 60:1 (1996), 105–109 |
42. |
S. B. Zaitseva, A. A. Zlotnik, “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, 6, 40–43 |
43. |
A. A. Amosov, A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 36:10 (1996), 1415–1428 |
44. |
A. A. Amosov, A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 36:2 (1996), 203–220 |
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1995 |
45. |
A. A. Amosov, A. A. Zlotnik, “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 ; Differ. Equ., 31:7 (1995), 1056–1066 |
46. |
A. A. Zlotnik, O. I. Kireeva, “On the error of some projection-grid methods for a fourth-order ordinary differential equation with nonsmooth data”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, 4, 49–61 ; Russian Math. (Iz. VUZ), 39:4 (1995), 45–57 |
47. |
A. A. Zlotnik, “Uniform estimates and stabilization of solutions to equations of one-dimensional motion of a multicomponent barotropic mixture”, Mat. Zametki, 58:2 (1995), 307–312 ; Math. Notes, 58:2 (1995), 885–889 |
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1994 |
48. |
A. A. Zlotnik, Nguen Zha Bao, “On the behavior as $t\to+\infty$ of solutions of a quasilinear nonstationary problem with free boundaries”, Differ. Uravn., 30:6 (1994), 1080–1082 ; Differ. Equ., 30:6 (1994), 1003–1005 |
49. |
A. A. Amosov, A. A. Zlotnik, “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 ; Differ. Equ., 30:4 (1994), 545–558 |
50. |
A. A. Zlotnik, “On estimates for the solutions of difference equations of the one-dimensional motion of a viscous barotropic gas”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, 9, 49–59 ; Russian Math. (Iz. VUZ), 38:9 (1994), 48–58 |
51. |
A. A. Amosov, A. A. Zlotnik, “Uniqueness and stability of generalized solutions for a class of quasilinear systems of composite type equations”, Mat. Zametki, 55:6 (1994), 13–31 ; Math. Notes, 55:6 (1994), 555–567 |
52. |
A. A. Zlotnik, Nguen Zha Bao, “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 ; Math. Notes, 55:5 (1994), 471–482 |
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1992 |
53. |
A. A. Amosov, A. A. Zlotnik, “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 ; Math. Notes, 52:2 (1992), 753–763 |
54. |
A. A. Zlotnik, “On one family of integral functionals”, Mat. Zametki, 52:1 (1992), 144–146 ; Math. Notes, 52:1 (1992), 741–743 |
55. |
A. A. Zlotnik, “Two-layer projection-difference method with a splitting operator for the wave equation”, Mat. Zametki, 51:4 (1992), 23–35 ; Math. Notes, 51:4 (1992), 342–350 |
56. |
A. A. Zlotnik, “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 ; Math. Notes, 51:3 (1992), 321–323 |
57. |
A. A. Zlotnik, “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 ; Comput. Math. Math. Phys., 32:4 (1992), 459–465 |
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1989 |
58. |
A. A. Amosov, A. A. Zlotnik, “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 ; U.S.S.R. Comput. Math. Math. Phys., 29:2 (1989), 129–139 |
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1987 |
59. |
A. A. Amosov, A. A. Zlotnik, “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 ; U.S.S.R. Comput. Math. Math. Phys., 27:4 (1987), 46–57 |
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1986 |
60. |
A. A. Amosov, A. A. Zlotnik, “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 |
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1985 |
61. |
A. A. Amosov, A. A. Zlotnik, “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 |
62. |
A. A. Zlotnik, I. D. Turetaev, “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 ; Math. USSR-Sb., 56:2 (1987), 529–544 |
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1984 |
63. |
A. A. Zlotnik, “Coefficient stability of systems of ordinary differential equations”, Differ. Uravn., 20:2 (1984), 220–229 |
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1983 |
64. |
A. A. Zlotnik, I. D. Turetaev, “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 |
65. |
A. A. Zlotnik, “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 |
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1982 |
66. |
A. A. Amosov, A. B. Borisov, V. D. Valedinskii, M. V. Vladimirov, Ya. M. Zhileikin, A. A. Zlotnik, M. A. Kuz'mina, “A set of routines for the solution of problems of nonlinear optics”, Zh. Vychisl. Mat. Mat. Fiz., 22:3 (1982), 756–758 ; U.S.S.R. Comput. Math. Math. Phys., 22:3 (1982), 275–277 |
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1980 |
67. |
A. A. Zlotnik, “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 ; U.S.S.R. Comput. Math. Math. Phys., 20:2 (1980), 155–164 |
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1979 |
68. |
A. A. Zlotnik, “A projection-difference scheme for the vibrating-string equation”, Dokl. Akad. Nauk SSSR, 245:2 (1979), 292–295 |
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1978 |
69. |
N. S. Bakhvalov, A. A. Zlotnik, “Coefficient stability of differential equations and averaging of equations with random coefficients”, Dokl. Akad. Nauk SSSR, 242:4 (1978), 745–748 |
70. |
A. A. Zlotnik, “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 ; U.S.S.R. Comput. Math. Math. Phys., 18:6 (1978), 92–104 |
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1977 |
71. |
A. A. Amosov, V. D. Valedinskii, Ya. M. Zhileikin, A. A. Zlotnik, “Description of a program set for solution of the light-wave propagation equations”, Zh. Vychisl. Mat. Mat. Fiz., 17:4 (1977), 1074–1076 ; U.S.S.R. Comput. Math. Math. Phys., 17:4 (1977), 253–256 |
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1984 |
72. |
A. A. Zlotnik, I. D. Turetaev, “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 |
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