Differential Equations, Vol. 37, No. 5, 2001, pp. 607–613. Translated from Differentsial’nye Uravneniya, Vol. 37, No. 5, 2001, pp. 579–585.Original Russian Text Copyright c© 2001 by Abrashin, Chetverushkin, Emel’yanov, Gaishun, Galanin, Gulin, Il’in, Kastomarov, Kurdyumov,Mazhorova, Moiseev, Mukhin, Petrov, Sadovnichii, Samarskii.

MEMBERSOF SCIENTIFIC COMMUNITY

Yurii Petrovich Popov(A Tribute in Honor of His Sixtieth Birthday)

On May 2, 2001, Professor Yurii Petrovich Popov, a dis-tinguished Russian scientist in applied mathematics, Doctor ofphysical-mathematical sciences, Corresponding Member of theRussian Academy of Sciences, celebrated his sixtieth birthday.

Yurii Petrovich Popov graduated with excellence from theDepartment of Aeromechanics of Moscow Institute of Physics andTechnology in 1964. After he had completed his postgraduatestudies, he was appointed to a position at the Institute for Ap-plied Mathematics of the Academy of Sciences of the USSR (nowM.V. Keldysh Institute for Applied Mathematics of the RussianAcademy of Sciences). Since then, his entire career has been asso-ciated with the institute. Popov defended his Ph.D. thesis in 1971and D.Sc. thesis in 1979 and became professor in 1981. In 1997,Russian Academy of Sciences elected him Corresponding Memberof the Division of Computer Science, Computing Machinery, andAutomation. Popov became a scientific secretary of the institutein 1975 and Deputy Director in 1980. He has been Directorof the Keldysh Institute for Applied Mathematics since 1999.

In 1964, Popov published his first article, written jointly with Petrov and Pukhnachev, in Zhur-nal vychislitel’noi matematiki i matematicheskoi fiziki (Journal of Computational Mathematics andMathematical Physics). Since then, he has published about 200 papers including 2 monographs,a discovery, and an invention. Many of Popov’s scientific results have become classical and belongto the toolbox of every qualified specialist in computational mathematics and mathematical mod-eling. Popov’s main scientific interests include numerical methods and mathematical modeling inproblems of magnetic and gas dynamics, astrophysics, electrodynamics, plasma physics, viscousfluid dynamics, and many other fields.

Popov’s broad, varied scientific interests have permitted him to succeed in using and developingone of the most important principles in the construction of numerical algorithms, expressed by therequirement that a numerical algorithm must be consistent with the nature of the phenomenonto be studied and that a discrete model must inherit the most significant properties of the phys-ical process. This principle underlies a new class of finite-difference approximations to problemsof mathematical physics, known as completely conservative schemes. The term was introduced inthe joint article [7] with Samarskii. Since then, numerous examples have shown that this class ofschemes offers some advantages over a variety of other classes. The complete conservativeness prin-ciple permits constructing schemes that provide good approximations to rapidly varying solutionseven on coarse grids, for which consistency is essentially lost. Such algorithms are particularly im-portant in modeling processes that involve numerous transitions between different forms of energy.The approach in which the passage to finite-difference approximations preserves balance relationsis presented most clearly in the 1975 monograph Raznostnye metody resheniya zadach gazovoidinamiki (Difference Methods for the Solution of Problems of Gas Dynamics) written jointly bySamarskii and Popov, which has been published in three editions.

Another important requirement imposed by Popov on numerical algorithms is that of homogene-ity (introduced by Tikhonov and Samarskii), which dramatically simplifies the logical structure ofthe computations and permits reducing random access memory requirements. Most finite-differenceapproximations constructed by Popov, as well as the corresponding algorithms, are homogeneous.The complete conservativeness and homogeneity principles are heuristic. This is due to the highcomplexity of the problems to be solved, which prevents one from carrying out a rigorous, mathe-matically perfect study.

0012-2661/01/3705-0607$25.00 c© 2001 MAIK “Nauka/Interperiodica”

608 ABRASHIN et al.

One of Popov’s hallmarks is his skill in using hierarchical sequences of model problems forsolving problems involving numerous diverse factors and phenomena. This permits extracting andcomprehensively studying the process in question and then including it in the description of theoverall complex process adequately. To this end, one must determine the “main character” of theproblem. (This role can be played by energy exchange, boundary conditions, external forces, etc.)

The monograph Kvazistatsionarnye elektromagnitnye polya v neodnorodnykh sredakh (Quasista-tionary Electromagnetic Fields in Inhomogeneous Media), written jointly with Galanin and dealingwith the construction, analysis, justification, and application of mathematical modeling meth-ods for processes occurring in various electrical equipment, can serve as an example of Popov’sapproach to the mathematical modeling of complicated phenomena in modern science and technol-ogy. Electrodynamic accelerators of massive objects, which provide high and superhigh velocities,are considered as specific examples in this book. The electrodynamic equations are used only asa basis of mathematical models for this class of problems. In reality, numerous factors can affectthe processes in such devices, including external electrical circuits, heat release, heat conduction,phase transitions, friction, etc. These factors are taken into account in the mathematical modelsand numerical algorithms developed in the book.

Popov’s investigations are inspired by real-life problems. On the one hand, he strives to performmathematical modeling alongside real experiments, thus complementing and helping to explainexperimental results. On the other hand, the permanent comparison of computed and experi-mental results allows one to construct physically meaningful mathematical models and numericalalgorithms related to the specific properties of real phenomenona.

The cycle of papers on the mathematical modeling of convective heat and mass transfer inmany-component media with phase transitions can be mentioned as an example. These studieshave been inspired by problems occurring in semiconductor technology, and the results have beenregistered as an invention.

An application of modern numerical methods to hierarchical models in computational astro-physics has led to fundamental results in supernova explosion theory as well as the theory describingthe formation and evolution of accretion disks in binaries. In particular, Popov and his coauthorshave shown the impossibility of a steady state of an accretion disk in a binary without mass inflowand the absence of spiral shock waves in the disk.

In 1969, a team including Popov, Tikhonov, Samarskii, and others received a discovery cer-tificate titled “The Phenomenon of Generation of a Self-Sustaining High-Temperature ElectricallyConducting Layer (T-layer) under a Nonstationary Motion of a Compressible Medium in a MagneticField.” The studies of the T-layer had required the development of new efficient computationaltechniques, in particular represented by completely conservative finite-difference approximations.At present, the T-layer phenomenon, which has passed the stage of theoretical investigation, is usedin various electrophysical devices.

Yurii Petrovich Popov has been awarded Order of the Badge of Honor and Order of the RedBanner of Labour. As a member of a team of authors, he was awarded the State Prize of the USSRin 1981 and the Prize of the Council of Ministers of the USSR in 1986.

Since 1971, Popov has been teaching actively. Numerous graduates of the Physical Departmentand the Department of Computational Mathematics and Cybernetics of M.V. Lomonosov MoscowState University are indebted to him for their knowledge in the field of computational mathematicsas well as the theory and practice of numerical methods. Many of his students have becomephilosophy doctors and several of them, doctors of sciences in physics and mathematics.

Popov is not only a scientist and a manager, but also a widely recognized popularizer of science.In this connection, we mention his recently republished book Matematika bez formul (Mathematicswithout Formulas) written jointly with Pukhnachev. Popov’s friends and colleagues know abouthis involvement in the KVN movement (the Club of Joyful and Ingenious) both as a member ofthe MIPT team and as an author of TV programs and admire him for his humor, sociability, andbenevolence.

We congratulate Yurii Petrovich Popov on his sixtieth birthday and wish him long fruitful life,happiness, health, new scientific results, new students, and success in everything.

V. N. Abrashin, B. N. Chetverushkin, S. V. Emel’yanov, I. V. Gaishun,N. P. Galanin, A. V. Gulin, V. A. Il’in, D. P. Kastomarov,

S. P. Kurdyumov, O. S. Mazhorova, E. I. Moiseev, S. I. Mukhin,A. A. Petrov, V. I. Sadovnichii, A. A. Samarskii

DIFFERENTIAL EQUATIONS Vol. 37 No. 5 2001

YURII PETROVICH POPOV 609

SELECTED SCIENTIFIC PUBLICATIONS OF YU. P. POPOV

1. Calculation by a Variational Method of the Eigenvibrations of Liquids in Fixed Containers (withA.A. Petrov and Yu.V. Pukhnachev), Zh. Vychislit. Mat. Mat. Fiz., 1964, vol. 4, no. 5, pp. 880–895.

2. Nonlinear Phenomenon of Generation of a Self-Sustaining High-Temperature Electrically ConductingGas Layer in Nonstationary Processes of Magnetohydrodynamics (with Tikhonov, A.N. et al.), Dokl.Akad Nauk SSSR, 1967, vol. 173, no. 4, pp. 808–810.

3. The T-Layer Phenomenon. Discovery (with Tikhonov et al.), 1968, no. 55.

4. Interaction of a Shock Wave with a Magnetic Field in a Medium with Finite Conductivity (withVolosevich, P.P. and Kurdyumov, S.P.), Izv. Akad. Nauk SSSR. Mekhanika Zhidkosti i Gaza, 1968,vol. 1, pp. 67–71.

5. Influence of the Finite Conductivity of a Medium on the Interaction of a Shock Wave with a MagneticField (with Volosevich, P.P. and Kurdyumov, S.P.), Izv. Akad. Nauk SSSR. Mekhanika Zhidkosti iGaza, 1968, vol. 4, pp. 15–22.

6. Effekt T-sloya v magnitnoi gidrodinamike (The T-Layer Phenomenon in Magnetohydrodynamics)(with Tikhonov, A.N. et al.), Moscow: IAM AS USSR, 1969.

7. Completely Conservative Difference Schemes for the Equations of Gas Dynamics and Magnetohydro-dynamics (with Samarskii, A.A.), Preprint IAM AS USSR, Moscow, 1969, no. 16.

8. Completely Conservative Difference Schemes (with Samarskii, A.A.), Zh. Vychislit. Mat. Mat. Fiz.,1969, vol. 9, no. 4, pp. 953–958.

9. Computation of a Heavy-Current Discharge in Lithium Plasma (with Volosevich, P.P. et al.), Dokl. naIX Mezhdunar. konf. po yavleniyam v ionizirovannykh gazakh (Abstr. IX Int. Conf. on Phenomenain Ionized Gases), Bucharest, 1969, pp. 36–39.

10. Completely Conservative Difference Schemes for the Equations of Magnetohydrodynamics (withSamarskii, A.A.), Zh. Vychislit. Mat. Mat. Fiz., 1970, vol. 10, no. 4, pp. 990–999.

11. On the Analysis of Gas-Ionizing Magnetohydrodynamic Shock Waves, Zh. Vychislit. Mat. Mat. Fiz.,1970, vol. 10, no. 5, pp. 1238–1246.

12. A Self-Similar Problem on a Heavy-Current Discharge in Plasma (with Volosevich, P.P., Kurdyumov,S.P., and Samarskii, A.A.), Zh. Vychislit. Mat. Mat. Fiz., 1970, vol. 10, no. 6, pp. 1447–1457.

13. Electrical Circuit Analysis in Magnetohydrodynamic Problems, Zh. Vychislit. Mat. Mat. Fiz., 1971,vol. 11, no. 2, pp. 449–461.

14. A Boundary Value Problem for Equations of Parabolic Type, Zh. Vychislit. Mat. Mat. Fiz., 1971,vol. 11, no. 4, pp. 1038–1042.

15. Completely Conservative Difference Schemes and Their Applications to the Numerical Analysis ofMagnetohydrodynamic Problems, Cand. Sci. (Phys.–Math.) Dissertation, Moscow, 1971.

16. Dynamics and Radiation of Rectilinear Heavy-Current Discharges in Air (with Aleksandrov, A.F.et al.), Zh. Eksperim. i Teoret. Fiz., 1971, vol. 61, no. 5, pp. 1841–1855.

17. A Magnetohydrodynamic Model of Nonstationary Acceleration of Plasma (with Samarskii, A.A. et al.),Dokl. Akad. Nauk SSSR, 1972, vol. 206, no. 2, pp. 307–310.

18. Stationary Modes of a Radiating Heavy-Current Self-Compressed Discharge in Plasma (with Dorod-nitsyn, V.A.), Zh. Vychislit. Mat. Mat. Fiz., 1973, vol. 13, no. 1, pp. 247–253.

19. Generation of T-Layers in Plasma Decelerated by a Magnetic Field (with Samarskii, A.A. et al.), Dokl.Akad. Nauk SSSR, 1974, vol. 216, no. 6, pp. 1254–1257.

20. The Analysis of Heavy-Current Discharges with Regard for the Secondary Breakdown (with Danilova,G.V. et al.), Preprint IAM AS USSR, Moscow, 1974, no. 6.

21. Numerical Modeling of the Secondary Breakdown in a Z-Pinch (with Samarskii, A.A. and Kurdyumov,S.P.), Dokl. II Mezhdunar. konf. po teorii plazmy: Sb. annotatsii dokl. (Abstr. II Int. Conf. onPlasma Theory), Kiev, 1974.

DIFFERENTIAL EQUATIONS Vol. 37 No. 5 2001

610 ABRASHIN et al.

22. The Role of Self-Organization of Pinch Discharges in Heating and Confinement of Plasma (with Kvar-tskhava, I.F. et al.), Sb. dokl. VIII konf. MAGATE po fizike plazmy i upravlyaemomu termoyadernomusintezu (Proc. VIII Conf. MAGATE in Physics of Plasma and Controlled Thermonuclear Synthesis),Tokyo, 1974, vol. 3, pp. 149–159.

23. Raznostnye skhemy gazovoi dinamiki (with Samarskii, A.A.) (Difference Schemes for Gas Dynamics),Moscow: Nauka, 1975.

24. The Magnetohydrodynamic Rotational Model of Supernovae Explosion (with Bisnovaty-Kogan, G.S.and Samokhin, A.A.), in Astrophysics and Space Sci., 1976, p. 34.

25. Thin Foil Heating by a Heavy-Current Electron Beam (with Bogolyubov, S.L. et al.), Pis’ma v Zh.Eksper. i Teoret. Fiz., 1976, vol. 24, no. 4, pp. 202–206.

26. Exit of Thermonuclear Neutrons from Plasma Compressed by a Shell (with Bogolyubskii, S.L. et al.),Pis’ma v Zh. Eksper. i Teoret. Fiz., 1976, vol. 24, no. 4, pp. 202–206.

27. The Analysis of Nonstationary Acceleration of Plasma with Regard to Dielectric Ablation (withGushchin, I.S. and Savichev, V.V.), Fizika Plazmy, 1976, vol. 2, no. 5, pp. 742–749.

28. Numerical Methods for One-Dimensional Nonstationary Problems of Gas Dynamics (with Samarskii,A.A.), Zh. Vychislit. Mat. Mat. Fiz., 1976, vol. 2, no. 5, pp. 1503–1518.

29. Process of Superhigh Matter Compression and Initiation of Thermonuclear Reaction by a PowerfulPulse Laser Radiation (with Volosevich, P.P. et al.), Fizika Plazmy, 1976, vol. 2, no. 6, pp. 883–897.

30. A Remark on the Analysis of Magnetohydrodynamic Problems with Regard for Phase Transitions(with Gushchin, I.S.), Zh. Vychislit. Mat. Mat. Fiz., 1977, vol. 17, no. 5, pp. 1248–1255.

31. The Convergence of Newton’s Iterative Method for the Solution of Difference Equations of Gas Dy-namics (with Samarskaya, E.A.), Zh. Vychislit. Mat. i Mat. Fiz., 1977, vol. 17, no. 1, pp. 276–280.

32. Some Problems of Gas Dynamics with Sources (with Poveshchenko, Yu.A.), Zh. Vychislit. Mat. Mat.Fiz., 1977, vol. 17, no. 4, pp. 1048–1056.

33. Completeness of Conservative Schemes for Two-Dimensional Equations of Gas Dynamics (withMazhorova, O.S.), Differents. Uravn., 1979, vol. 15, no. 7, pp. 1318–1331.

34. A Remark on the Analysis of One-Dimensional Nonstationary Problems of Gravitational Gas Dynamics(with Kosovichev, A.G.), Zh. Vychislit. Mat. Mat. Fiz., 1979, vol. 19, no. 5, pp. 1253–1261.

35. Numerical Methods and Mathematical Modeling of Magnetohydrodynamic Processes, Doctoral(Phys.–Math.) Dissertation, Moscow, 1979.

36. Investigation of Magnetorotational Supernova Explosion in the Cylindrical Model (with Ardelyan,N.V. and Bisnovatyi-Kogan, G.S.), Astr. Zh., 1979, vol. 56, no. 6, pp. 1244–1255.

37. Interaction of Dissipative Heat Structures in Nonlinear Media (with Kurdyumov, S.P. et al.), Dokl.Akad. Nauk SSSR, 1980, vol. 251, no. 4, pp. 836–839.

38. Numerical Modeling of the Dynamics of Heating and Dispersion of Matter in Absorption of a Heavy-Current Relativistic Electron Beam (with Koldoba, A.V. et al.), Differents. Uravn., 1980, vol. 16,no. 7, pp. 1235–1244.

39. Numerical Methods for the Navier–Stokes Equations (with Mazhorova, O.S.), Zh. Vychislit. Mat.Mat. Fiz., 1980, vol. 20, no. 4, pp. 1005–1020.

40. Raznostnye metody resheniya zadach gazovoi dinamiki (with Samarskii, A.A.) (Difference Methodsfor the Solution of Problems of Gas Dynamics), Moscow: Nauka, 1980.

41. Peculiarities of the Solution of Equations of Gas Dynamics by Finite-Difference Methods (with Popov,S.B.), Differents. Uravn., 1981, vol. 17, no. 4, pp. 719–731.

42. Evolution of MHD-Waves in a Homogeneous Isothermal Medium (with Bisnovatyi-Kogan, G.S. andPopov, S.B.), Astrofizika, 1981, vol. 17, no. 2, pp. 333–348.

43. Matrix Iteration Method for Numerical Solution of Two-Dimensional Navier–Stokes Equations(with Mazhorova, O.S.), Dokl. Akad. Nauk SSSR, 1981, vol. 259, no. 3, pp. 535–540.

DIFFERENTIAL EQUATIONS Vol. 37 No. 5 2001

YURII PETROVICH POPOV 611

44. On Quasiperiodic Oscillations in the Solar Atmosphere, Izv. Krym. Astrofiz. Observatorii , 1981,vol. 13, pp. 15–24.

45. Numerical Solution of Problems of Concentration Convection (with Mazhorova, O.S.), in Matemati-cheskie modeli, analiticheskie i chislennye metody v teorii perenosa (Mathematical Models and Ana-lytic and Numerical Methods in Transport Theory), Minsk: ITMO AS BSSR, 1982, pp. 144–152.

46. Numerical Experiments on the Theta Pinch (with Busurina, L.N. et al.), Fizika Plazmy, 1982, vol. 8,no. 5, pp. 1053–1062.

47. Approximation of Differential Operators on Nonorthogonal Grids (with Koldoba, A.V. and Pove-shchenko, Yu.A.), Differents. Uravn., 1982, vol. 19, no. 7, pp. 1235–1245.

48. Numerical Modeling of Heat Processes in Compounds of Heterogeneous Materials (with Maksimov,A.V. et al.), Differents. Uravn., 1982, vol. 18, no. 7, pp. 1244–1251.

49. Iterative Methods for the Solution of Difference Schemes for Equations of Gas Dynamics with HeatConduction (with Poveshchenko, Yu.A. and Samarskaya, E.A.), Zh. Vychislit. Mat. Mat. Fiz., 1982,vol. 22, no. 4, pp. 903–912.

50. Difference Schemes with Artificial Dispersion (with Mukhin, S.I. and Popov, S.B.), Zh. Vychislit.Mat. Mat. Fiz., 1983, vol. 23, no. 6, pp. 1355–1369.

51. Numerical Modeling of Growing Monocrystalline Layers of Semiconductors by the Liquid-Phase Epi-taxy Method (with Mazhorova, O.S. et al.), Fizika i Khimiya Obrabotki Materialov , 1983, no. 4,pp. 81–90.

52. Investigation of Internal Dissipative and Dispersion Properties of Difference Schemes (with Mukhin,S.I. and Popov, S.B.), in Aktual’nye problemy matematicheskoi fiziki i vychislitel’noi matematiki(Topical Problems of Mathematical Physics and Computational Mathematics), Moscow: Nauka, 1984,pp. 134–144.

53. Invention (with Tvirova, E.A. et al.), Inventor’s Certificate no. 213137.

54. An Algorithm for Solving the Heat Equation on Nonorthogonal Grids (with Koldoba, A.V. andPoveshchenko, Yu.A.), Differents. Uravn., 1985, vol. 21, no. 7, pp. 1273–1276.

55. Continuous Self-Similar and Periodic Solutions of the Shallow Water Equations (with Gogodze, I.K.and Khutsishvili, V.V.), in Nakat tsunami na bereg (Cunami Rolling on Coast), Gor’kii: IAF ASUSSR, 1985, pp. 11–21.

56. Traveling Waves in a Compressible Medium with Nonlinear Energy Sources and Sinks (with Koso-vichev, A.G.), Differents. Uravn., 1986, vol. 22, no. 7, pp. 1213–1220.

57. A Matrix Algorithm for the Numerical Solution of Nonstationary Problems of Concentration Con-vection for Many-Component Media (with Mazhorova, O.S. and Pokhilko, V.I.), in Mat. Mode-lirovanie. Poluchenie monokristallov i poluprovodnikovykh struktur (Mathematical Modeling. Obtain-ing Monocrystals and Semiconducting Structures), Moscow: Nauka, 1986, pp. 19–31.

58. Numerical Analysis of Convective Mass Transfer in the Production of Semiconductor Structures bythe Liquid-Phase Epitaxy Method (with Dmitrieva, L.A. et al.), in Mat. Modelirovanie. Polucheniemonokristallov i poluprovodnikovykh struktur (Mathematical Modeling. Obtaining Monocrystals andSemiconducting Structures), Moscow: Nauka, 1986, pp. 84–101.

59. Two-Layer Completely Conservative Difference Schemes for Equations of Gas Dynamics in EulerVariables (with Koldoba, A.V. and Poveshchenko, Yu.A.), Zh. Vychislit. Mat. Mat. Fiz., 1987,vol. 27, no. 5, pp. 779–784.

60. Investigation of Algorithms for the Numerical Solution of Systems of Parabolic Equations with Non-linear Boundary Conditions (with Mazhorova, O.S. and Pokhilko, V.I.), Differents. Uravn., 1987,vol. 23, no. 7, pp. 1240–1249.

61. A Diffusion Model of Epitaxial Growth of Solid Solution from a Bounded Melt (with Karpov, S.Yu.et al.), Zh. Teoret. Fiziki , 1988, vol. 58, no. 2, pp. 355–362.

62. Conditions for the Onset of High-Temperature and High-Current-Density Zones in the Solar Atmo-sphere (with Boiko, A.Ya. et al.), Izv. Krym. Astrofiz. Observatorii , 1988, vol. 29, pp. 18–31.

DIFFERENTIAL EQUATIONS Vol. 37 No. 5 2001

612 ABRASHIN et al.

63. Numerical Analysis of Fluid Electrophoresis without Supporting Media (with Mazhorova, O.S. et al.),Izv. Akad. Nauk SSSR. Mekhanika Zhidkosti i Gaza, 1988, no. 3, pp. 14–20.

64. On Numeral Simulation of Free Fluid Electrophoresis (with Ermakov, S.V. and Mazhorova, O.S.)Proc. Int. Symp. on Hyromech and Heat., 1991, pp. 409–413.

65. Raznostnye metody resheniya zadach gazovoi dinamiki (with Samarskii, A.A.) (Difference Methodsfor the Solution of Problems of Gas Dynamics), Moscow: Nauka, 1992, 2nd ed.

66. Star Evolution and Mass Transfer in Binaries (with Bojarchuk, A.A. et al.), Vien, Austria, 1992, p. 2(Report on IAU Collog: 137).

67. Mathematical Simulation of Multidimensional Electronetic Field in Spheres with Sharply Nonhomo-geneous Electromagnetic Qualities (with Galanin, M.P. and Mukhin, S.I.), in Math. Model. and Appl.Math., Elsevier Sci. Publ. B. V. (North Holland), 1992, pp. 173–182.

68. Finite-Difference Algorithm for Convection Diffusion Equation Applied to Electrophoresis Problem(with Ermakov, S.V. and Mazhorova, O.S.), Informatica, 1992, vol. 3, no. 2, pp. 173–197.

69. Mathematical Modeling of Problems of Electrophoretic Separation of Biological Mixtures. I (withErmakov, S.V. and Mazhorova, O.S.), Differents. Uravn., 1992, vol. 28, no. 10, pp. 1810–1821.

70. Mathematical Modeling of Problems of Electrophoretic Separation of Biological Mixtures. II (withErmakov, S.V. and Mazhorova, O.S.), Differents. Uravn., 1992, vol. 28, no. 12, pp. 2129–2137.

71. Taking Account of External Electrical Circuits in Interior Problems of Electrodynamics (with Galanin,M.P. and Mukhin, S.I.), Mat. Modelirovanie, 1993, vol. 5, no. 9, pp. 80–97.

72. The Influence of the Boundary Parameters of Stellar Wind on the Structure of Matter Flow in Binarieswith Components Not Filling the Rosch Cavity (with Bisikalo, D.V. et al.), Astr. Zh., 1994, vol. 71,no. 4, pp. 560–571.

73. The Structure of the Accretion Disk in Binaries with Components Not Filling the Rosch Cavity (withBisikalo, D.V. et al.), Astr. Zh., 1995, vol. 72, no. 2, pp. 190–202.

74. The Structure of Accretion Disk in Symbiotic Stars. The Isothermal Case (with Bisikalo, D.V. et al.),Astr. Zh., 1995, vol. 72, no. 3, pp. 367–373.

75. Spatially Three-Dimensional Computations of Electrodynamic Acceleration of Conducting Bodies(with Ignatko, V.P. et al.), Zh. Tekh. Fiziki , 1995, vol. 65, no. 6, pp. 9–20.

76. Kvazistatsionarnye elektromagnitnye polya v neodnorodnykh sredakh. Matematicheskoe modelirovanie(with Galanin, M.P.) (Quasistationary Electromagnetic Fields in Heterogeneous Media. MathematicalModeling), Moscow: Nauka, 1995.

77. Stationary Disk Structures Near Gravitating Compact Objects (with Abakumov, M.V. et al.), Astr.Zh., 1996, vol. 73, no. 3, pp. 407–418.

78. Mathematical Model of the Electrokinetic Method for Soil Purification (with Konstantinov, L.V.et al.), Preprint M.V. Keldysh IAM RAS , Moscow, 1996, no. 68.

79. Mathematical Modeling of Electrokinetic Purification of Fluids in Membrane Devices (with Karlin,Yu.V. et al.), Preprint M.V. Keldysh IAM RAS , Moscow, 1996, no. 69.

80. The Influence of the Parameters of the External Conductive Housing on the Body Acceleration inan Electrodynamic Accelerator (with Galanin, M.P. et al.), Zh. Tekh. Fiziki , 1996, vol. 66, no. 10,pp. 198–206.

81. The Stability of a Finite-Difference Problem for a System of Parabolic Equations with NontraditionalBoundary Conditions (with Mazhorova, O.S. and Sakharchuk, A.S.), Differents. Uravn., 1997, vol. 33,no. 7, pp. 946–954.

82. The Interaction of Shock Wave with a Compact Gravitating Object (with Popov, S.B. and Chechetkin,V.M.), Mat. Modelirovanie, 1997, vol. 9, no. 1, pp. 40–54.

83. The Stability of Difference Schemes for a System of Parabolic Equations (with Mazhorova, O.S. andSakharchuk, A.S.), Preprint M.V. Keldysh IAM RAS , Moscow, 1997, no. 90.

DIFFERENTIAL EQUATIONS Vol. 37 No. 5 2001

YURII PETROVICH POPOV 613

84. Gasdynamic Processes in the Accretion Disk of a Binary (with Abakumov, M.V. et al.), Mat. Mode-lirovanie, 1998, vol. 10, no. 5, pp. 35–46.

85. Asymptotic Stability of Difference Schemes for a System of Parabolic Equations with NontraditionalBoundary Conditions (with Mazhorova, O.S. and Sakharchuk, A.S.), Differents. Uravn., 1999, vol. 35,no. 2, pp. 249–256.

86. Numerical Modeling of Spatially Three-Dimensional Phenomena for the Electromagnetic Accelerationof Conducting Macrobodies (with Galanin, M.P et al.), Mat. Modelirovanie, 1999, vol. 11, no. 8,pp. 3–22.

87. Some Problems of Gravitational Gas Dynamics (with Abakumov, M.V. et al.), Mat. Modelirovanie,2000, vol. 12, no. 5, pp. 11–120.

88. Mathematical Modeling of the Production of Triple Semiconductors by the Liquid-Phase EpitaxyMethod (with Mazhorova, O.S.), Vest. MGTU. Estestvennye Nauki , 2000, no. 2, pp. 37–53.

DIFFERENTIAL EQUATIONS Vol. 37 No. 5 2001