Professor, Dr. Sergey V. Meleshko
Complete List of 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)
(psfile)
(with N.Manganaro) in press
 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)
1990
 On potential polytropic gas flows of triple
waves.
Prikl. matem. and mech., 1990, 54, 5. pp.775779.
(English transl. in J.Appl.Maths Mechs, 1990, v.54, No.5.)
 Double waves in ideal rigidplastic body with a plane
deformation.
Journ.prikl.mech.i techn.phyz, 1990, 2.
pp.131136.
 Group theoretical analysis of the kinetic Boltzmann
equation and its models.
Arch. Mech., 1990, v.42, No.6,
pp.693701.
(with Yu.N.Grigoriev)
 Application of REDUCE system for analysis of
consistency of systems of P.D.E.'s.
Proceedings of the
international symposium on symbolic and algebraic computation (ISSAC'90).
Tokyo. 1990, p.301.
(with V.G.Ganzha, V.P.Shelest)
1989
 On nonisoentropic steady space and plane
unsteady double waves.
Prikl. matem. and mech., 1989, 53, 2.
pp.255260. (English transl. in J.Appl.Maths Mechs, 1989, v.53, No.2.)
 About multiple waves of gas dynamics equations and
theory of plasticity.
International conference on algebra,
devoted to A.I.Malcev anniversary. Abstracts. Novosibirsk, 1989. p.30.
 Group theoretical analysis of the kinetic Boltzmann
equation and its model.
XIX Biennial symposium on advanced
problems and methods in fluid mechanics. Kozubnic (Poland). 1989. p.235.
(with Yu.N.Grigoriev)
 Intermediate calculations in analytical investigation
of differential equations (on computer).
Modelirovanie v
mechanike. Novosibirsk, 1989, 3(20), 4. pp.4958.
(with V.G.Ganzha, V.P.Shapeev)
 Application of computer algebra to the analysis of
compatibility of partial differential equations.
International
conference on algebra, devoted to the A.I.Malcev anniversary. Abstracts.
Novosibirsk, 1989. p.18.
(with V.G.Ganzha, V.P.Shapeev)
 A study of compatibility a system of differential
equations on a computer.
Abstracts of the conference
"Mathematical methods in mechanics". Novosibirsk, 1989. p.15.
(with V.G.Ganzha, V.P.Shapeev)
1988
 On plane flows of a double wave type.
Modelirovanie v mechanike, Novosibirsk, 1988, 2(19), 2.
pp.111118.
 On group properties of viscoelastic media motion
equations.
Modelirovanie v mechanike, Novosibirsk, 1988,
2(19), 4. pp.116126.
 Double waves of gas dynamics equations with three
independent variables.
Modern problems of fluid dynamics and
gas. Abstracts, 1988. p.130.
 Method of differential constraints.
Nikolay Nikolaevich Yanenko. Essaies, articles and reminiscence.
Novosibirsk, Nauka, 1988. pp.107115.
(with V.P.Shapeev)
 Approximate kinetic model of overheated relaxation in
a gas.
Abstracts of presentations of IX national conference on
dynamics of rarefied gas. 1987, vol.1, Sverdlovsk. p.26.
(with Yu.N.Grigoriev, A.N.Mikhalicyn)
 A study of an approximate kinetic model of gas
relaxation for overheated energies of molecules.
Modelirovanie v
mechanike, Novosibirsk, 2(19), 5. pp.4552.
(with Yu.N.Grigoriev, A.N.Mikhalicyn)
1987
 Group analysis of the integrodifferential
Boltzmann equation.
Dokl. Acad. Nauk S.S.S.R., 1987, 297, 2.
pp.323327.
(with Yu.N.Grigoriev)
1986
 Comparisons of solutions of one model problem of
simplified and complete equations of a viscous heat conduction gas.
Chisl.metody mech.splosh.sredy, Novosibirsk, 1986, 17, 3.
pp.115123.
 An analytical and numerical study of compressible
flows based on the parabolized NavierStokes equations.
The IY
international conference on boundary and interior layers (BAILIY).
Abstracts. 1986, p.93.
(with S.G.Cherny)
 An investigation of invariant solutions of the
Boltzmann kinetic equation and its models.
Preprint of Institute
of Theoretical and Applied Mechanics, 1986, 1886. 51 pp.
(with Yu.N.Grigoriev)
 An application of differential constraints method for
description of wave propagation in elasticviscoplastic medium.
Sixth national meeting on theoretical and applied mechanics.
Abstracts and presentations, 1986. p.450.
(with V.P.Shapeev)
1985
 A classification of a plane isentropic gas flow
of a double wave type.
Prikl. matem. and mech., 1985, 49, 3.
pp.406410. (English transl. in J.Appl.Maths Mechs, 1985, v.49, No.3.)
 Invariant solutions of the parabolized NavierStokes
compressible gas equations.
Theoretical and applied problems of
the computational mathematics and mathematical physics. Riga. 1985,
pp.173174.
 An investigation of viscous compressible flows based
on the parabolized NavierStokes equations.
Preprint of
Institute of Theoretical and Applied Mechanics, 1985, 3285. 47 pp.
(with S.G.Cherny)
1984
 A stress wave propagation of a simple wave type
in an elasticviscoplastic media.
Chisl. meth. resh. zadach of
the theory of elastic and plastic. Novosibirsk. 1984, pp.205211.
 Method of differential constraints.
Physical mechanics of inhomogeneous media. Novosibirsk. 1984,
pp.313.
(with V.P.Shapeev, N.N.Yanenko)
1983
 Differential constraints and oneparameter
LieBacklund transformation groups.
Dokl. AS USSR, 1983,
271, 1. pp.4246; (English transl., Soviet Math. Dokl., 28, 3741).
 About jointing of DPsolutions over strong
discontinuity.
Chisl.metody and the problem of optimization,
Tomsk, 1983, pp.1523.
(with V.P.Shapeev)
 Using a computer for analysis of compatibility of
systems of partial differential equations.
Analytical
computations on a computer and their applications in theoretical physics.
Dubna, JINR. 1983, pp.125131.
(with V.G.Ganzha, F.A.Murzin, V.P.Shapeev, N.N.Yanenko)
 Symbolic manipulations and their applications for
constructing new exact solutions and different schemes.
Proceedings of Symp. on numerical solutions of nonlinear problems.
Paris, 1983, pp.314329.
(with V.G.Ganzha, S.I.Mazuric, V.P.Shapeev, N.N.Yanenko)
1982
 Symbolic manipulations in methods for solving
problems in mathematical physics.
Symp. Mathematics for computer
science. Paris. 1982. pp.431438.
(with A.N.Valiullin, V.G.Ganzha, F.A.Murzin,
V.P.Shapeev, N.N.Yanenko)
 One problem about decay arbitrary discontinuity.
Chisl.metody mech. splosh.sredy, Novosibirsk, 1982, 13, 6.
pp.7785.
(with V.P.Shapeev, N.N.Yanenko)
 Analysis compatibility of systems of partial
differential equations.
Preprint of Institute of Theoretical and
Applied mechanics, 1982, N 2082. pp.2425.
(with V.G.Ganzha, F.A.Murzin, V.P.Shapeev, N.N.Yanenko)
 Symbolic manipulations in methods for solving
problems in mathematical physics.
Complex of programs in
mathematical physics. Institute of Theoretical and Applied Mechanics, 1982.
pp.123129.
(with A.N.Valiullin, V.G.Ganzha, F.A.Murzin, V.P.Shapeev, N.N.Yanenko)
 The problem of breakdown of an arbitrary
discontinuity.
The IUTAM Symp. nonlinear deformation waves.
Abstracts. Tallin. 1982. p.33.
(with V.P.Shapeev, N.N.Yanenko)
1981
 A solution of a wave problem for dynamics of
inelastic continuous medium by method of differential constraints.
Ph.D. thesis, 1981, Institute of Hydrodynamics. Novosibirsk.
 One class of solutions of systems of quasilinear
differential equations with many independent variables.
Chisl.metody mech.splosh.sredy, Novosibirsk, 1981, 12, 4.
pp.87100.
 Realization on computer an algorithm for studying
consistency of systems of partial differential equations.
Dokl.
AS USSR, 1981, 261, 5. pp.10441046.
(with V.G.Ganzha, F.A.Murzin, V.P.Shapeev, N.N.Yanenko)
1980
 DPconditions and a joining problem of different
DPsolutions.
Chisl.metody mech.splosh. sredy, Novosibirsk,
1980, 11, 6. pp.96109.
 Method of differential constraints and a problem of
decay an arbitrary discontinuity.
Preprint of Institute of
Theoretical and applied mechanics, 1980, No. 47, pp.2425.
 Method of differential constraints and a problem of
decay an arbitrary discontinuity.
Dokl. AS USSR, 1980, 254,
4, pp.796798 (Soviet Math. Dokl., 1980, 22, 2, pp.447449.)
(with V.P.Shapeev, N.N.Yanenko)
 The Goursat problem for nonhomogeneous systems of
differential equations.
Chisl.metody mech.splosh.sredy,
Novosibirsk, 1980, 11, 7. pp.109117.
(with V.P.Shapeev)
1979
 An application of DPsolutions to the problem of
decay an arbitrary discontinuity in inelastic continuous media.
Chisl.metody mech.splosh.sredy, Novosibirsk, 1979, 10, 6.
pp.8596.
(with V.P.Shapeev)
1977
 One method of defining a state equation.
Chisl.metody mech.splosh.sredy, Novosibirsk, 1977, 8, 1.
pp.8387.
(with V.P.Shapeev)
Page Last Updated 22 June, 2002