Professor, Dr. Sergey V. Meleshko
List of Recent Publications
2002

A truncated Painleve expansion associated with the Tzitzeica equation:
Consistency and general solution.
Physics Letters A
(psfile)
(with W.K.Schief) in press
 Reduction Procedure and Generalized Simple Waves for
Systems Written in the Riemann Variables.
Nonlinear Dynamics (An International Journal
of Nonlinear Dynamics and Chaos in Engineering Systems)
2002, 30 (1), pp.87102
(psfile)
(with N.Manganaro)
 A particular class of partially invariant solutions
of the NavierStokes equations.
European J. of Applied
Mathematics (sent)
(psfile)
 Rotationally Invariant and Partially Invariant Flows
of a Viscous Incompressible Fluid and a Viscous Gas.
Nonlinear Dynamics (An International Journal
of Nonlinear Dynamics and Chaos in Engineering Systems)
2002 v. 28, pp.105124
(psfile)
(with A.Hematulin)
 Group classification of twodimensional steady
viscous gas dynamics equations with arbitrary state equations.
J.Phys. A: Math. Gen., 2002, 35, pp.35153533.
(PDFfile)
2001
 Classification of invariant solutions of the
full Boltzmann equation.
Proceedings "WASCOM 99" 10th
Conference on Waves and Stability in Continuous Media (712th June, 1999,
Italy).
Editors Vincenzo Ciancio, Andrea Donato, Francesco Oliveri, Salvatore Rionero.
World Scientific, Singapore. 2001, pp.219233.
(psfile)
(with Yu.N.Grigoriev)
 Group Classification and Representations of Invariant
Solutions of the full Boltzmann Equation.
Rarefied Gas Dynamics.
22nd International Symposium, Sydney, Australia (914 July 2000). Editors
Timothy J.Bartel and Michael A.Gallis, Melville, New York, 2001, pp.109116.
(psfile)
(with Yu.N.Grigoriev)
2000
 On compatibility of overdetermined systems for
double waves.
Nonlinear Dynamics (An International Journal
of Nonlinear Dynamics and Chaos in Engineering Systems), 2000 v. 22, 1,
pp.8599.
(psfile)
 Application of computer algebra to analysis of
differential equations systems compatibility.
6th IMACS
International IMACS Conference on Applications of Computer Algebra IMACS ACA
2000, June, 2528, 2000, St. Petersburg, Russia  Abstracts, pp.3738.
in Russian (with V.P.Shapeev)
1999
 One class of partially invariant solutions of
the NavierStokes equations.
Journal of applied mechanics and
technical physics. 1999, 40, 2, pp.2433.
(psfile)
(with V.V.Pukhnachov)
 Classification of invariant solutions of the
Boltzmann equation.
Journal of Physics A: Mathematical and
General. 1999, 32, 28 (16 July 1999), pp.337343.
(PDFfile)
(with Yu.N.Grigoriev, P.Sattayatham)
 An application of the differential constraints method
for the twodimensional equations of gas dynamics.
Prikl. matem.
and mech., 1999, 63, 6, pp.909916. (English transl. in J.Appl.Maths Mechs,
1999, v.63, 6. pp.885891)
(PDFfile)
(with V.P.Shapeev)
1998
 Group analysis of the Boltzmann equations of a
relaxative multicomponent gas.
Dokl. Acad. Nauk Russia,
1998, 360 (4).
(psfile)
(with Yu.N.Grigoriev)
 BobylevKrookWu Modes for Multicomponent Gas
Mixtures.
Physical Review Letters, 1998, v.81 (1), pp.9395
(PDFfile)
(with Yu.N.Grigoriev)
 Group classification of twodimensional stable
viscous gas equations.
International Journal of NonLinear
Mechanics, 1998, v.34, 3, pp.449456.
(PDFfile)
 Symmetry and multiple waves in gas dynamics.
Lecture notes of the joint ISAMM/FRD interdisciplinary Workshop on
Symmetry analysis and mathematical modeling.
International Institute for Symmetry Analysis and Mathematical Modeling at
University of NorthWest (South Africa). 1998.
(psfile)
 Application of group analysis in gas kinetics.
Lecture notes of the joint ISAMM/FRD interdisciplinary Workshop on
Symmetry analysis and mathematical modeling. International Institute for
Symmetry Analysis and Mathematical Modeling at University of NorthWest (South
Africa). 1998.
(psfile)
1997
 Steady spatial nonisentropic
doublewave type gas flows.
Prikl. Matemat. i Mekhanika. 1997, 61, 1. pp.159167.
(English transl. in J.Appl.Maths Mechs, 1997, v.61 (1).)
(PDFfile)
 Group classification of threewave equations in
nonlinear optics.
International Conference on Modern
Group Analysis (MOGRAN YII), Developments in Theory, Computation and
Application, Nordfjord, (Norway), MARS Publishers, 1997. pp.219226.
(psfile)
(with A.V.Gorchakov)
 Application of Group Analysis to the Boltzmann
equation.
Proceedings of International conference on
Computational Mathematics (ICCM'97), Bangkok. pp.189194.
(with Yu.N.Grigoryev, N.P.Moshkin, P.Sattayatham, E.Schulz,
S.Tangmanee)
1996
 Generalization of equivalence transformations.
Journal of Nonlinear mathematical physics, 1996, 3 (12).
pp.170174.
(PDFfile)
 Group classification gas dynamics equations with
constant body forces.
Journal of applied mechanics and technical
physics. 1996, 1.
(psfile)
 Unsteady space nonisentropic flows of a double wave
type.
Journal of applied mechanics and technical physics.
1996, 2.
 Lie group and invariant solutions of the system of
kinetic Boltzmann equations.
Proceedings of International
conference "Modern problems in mathematics and mechanics" in honor
P.L.Chebyshev's 175 anniversary. Moscow, Department of mechanics and
mathematics of Moscow state university, 1996, vol.1. pp.125128.
(psfile)
(with Yu.N.Grigoriev)
 Group analysis of the Boltzmann equations of a
spatially uniform multicomponent gas.
International Conference
on the Methods of Aerophysical Research (ICMAR), Proceedings, part 1, 1996.
pp.139144.
(with Yu.N.Grigoriev)
 Lie groups and invariant solutions of the system of
Boltzmann equations.
International conference "Mathematical
models and numerical methods of continuum mechanics", 1996, Novosibirsk.
pp.4344.
(with Yu.N.Grigoriev)
 An application of the method of differential
constraints to twodimensional gas dynamics equations.
International Conference on the Methods of Aerophysical Research,
ICMAR, Proceedings, Part 3, 1996, pp.221226.
(with V.P.Shapeev)
 An application of the method of differential
constraints to twodimensional gas dynamics equations.
International conference "Mathematical models and numerical methods
of continuum mechanics", 1996, Novosibirsk. pp.7879.
(with V.P.Shapeev)
1995
 On double waves of equations with three
independent variables.
Dokl. AS Russian, 1995, 345, 6.
(psfile)
 Group analysis of kinetic equations.
Russian Journal Numerical Analysis and Mathematical Modeling,
1995, v.9 (5).
(with Yu.N.Grigoriev)
 Group analysis of kinetic models.
International conference "Advanced Mathematics, Computations and
Applications", 1995. pp.172178.
(with Yu.N.Grigoriev)
 Calculation of symmetry groups for
integrodifferential equations.
CRC Handbook of Lie Group
Analysis of Differential Equations vol. 3, New Trends, 1995. pp.139145.
(with N.H.Ibragimov)
 Differential constraints.
CRC Handbook
of Lie Group Analysis of Differential Equations vol. 3, New Trends, 1995.
pp.283289.
(with N.H.Ibragimov)
1994
 Homogeneous autonomous systems with three
independent variables.
Prikl. matem. and mech., 1994, 58, 5.
pp.97102. (English transl. in J.Appl.Maths Mechs, 1994, v.58, No.5,
pp.857863.).
(psfile)
 Group classification of the twodimensional gas
dynamics equations.
Prikl. matem. and mech., 1994, 58, 4.
pp.5662. (English transl. in J.Appl.Maths Mechs, 1994, v.58, No.4,
pp.629635.)
(psfile)
 One class of partial invariant solutions of plane gas
flows.
Differential equations, 1994, 30, 10.
(psfile)
 Reduction of double waves of homogeneous autonomous
systems.
Seminar on analytic methods of gas dynamics and
optimization SAMGOP94. Ekaterinburg. Abstracts. 1994. pp.80.
 Reduction of double waves of homogeneous autonomous
systems.
Siberian conference on applied and industrial
mathematics. Abstracts, Engineering mathematics section, subsection
"Mathematics in new engineering technology". Novosibirsk, 1994. pp.5758.
1993
 Methods for constructing exact solutions of
continuum mechanics equations.
Textbook, Novosibirsk state
university, 1993.
(psfile)
 Application of REDUCE system for analysis of
compatibility of partial differential equations.
Modelirovanie v
mechanike, Novosibirsk, 1993, 7(24), 4. pp.2635.
(with V.G.Ganzha, Shapeev V.P.)
 Influence of rarefaction on mass transfer in a
plasmachemical reactor.
Computational technologies, 1993,
v.2, 7. pp.4754.
(with Yu.N.Grigoriev)
1992
 Influence of mass transfer on homogeneity in a
planar reactor.
Surface, 1992, 12. pp.6068.
(with M.R.Baklanov, Grigoryev Yu.N., V.G.Pluhin)
 Automation of compatibility analysis of quasilinear
PDE systems with the aid of the REDUCE system.
Computer Algebra
and Its Applications to Mechanics, 1992, pp.8995.
(with V.G.Ganzha, V.P.Shapeev)
1991
 Classification of solutions with degenerate
hodograph of the gas dynamics and plasticity equations.
Doctoral
thesis, Sverdlovsk, 1991.
 On solutions with degenerate hodograph of the
quasisteady equations of the theory of plasticity with the Mises flow
condition.
Journ.prikl.mech.i techn.phyz, 1991, 1. pp.8288.
 On doublewavetype plane gas flows.
Russian Journal of Theoretical and Applied Mechanics, v.1, No.1,
1991, pp.4754.
 Group theoretical analysis of some kinetic equations.
Modelirovanie v mechanike, Novosibirsk, 1991, 5(22), 3.
pp.2739.
(with Yu.N.Grigoriev)
 Influence of rarefaction on mass transfer in a
plasmachemical reactor.
Dynamics of rarefied gas. IX
National conference. Abstracts, 1991
(with Yu.N.Grigoriev)
 Application of REDUCE system for analysis of
compatibility of partial differential equations.
Preprint Inst
of Heat Physics AS Ukrainian SSR, No.9084P, Kiev, 1991.
(with V.G.Ganzha, S.S.Moskaluk, V.P.Shapeev, V.P.Shelest)
Page Last Updated 22 June, 2002