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 (ps-file) (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.87-102 (ps-file) (with N.Manganaro)

A particular class of partially invariant solutions of the Navier-Stokes equations.
European J. of Applied Mathematics (sent)

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.105-124 (ps-file) (with A.Hematulin)

Group classification of two-dimensional steady viscous gas dynamics equations with arbitrary state equations.
J.Phys. A: Math. Gen., 2002, 35, pp.3515-3533. (PDF-file)

2001

Classification of invariant solutions of the full Boltzmann equation.
Proceedings "WASCOM 99" 10-th Conference on Waves and Stability in Continuous Media (7-12th June, 1999, Italy). Editors Vincenzo Ciancio, Andrea Donato, Francesco Oliveri, Salvatore Rionero. World Scientific, Singapore. 2001, pp.219-233. (ps-file) (with Yu.N.Grigoriev)

Group Classification and Representations of Invariant Solutions of the full Boltzmann Equation.
Rarefied Gas Dynamics. 22-nd International Symposium, Sydney, Australia (9-14 July 2000). Editors Timothy J.Bartel and Michael A.Gallis, Melville, New York, 2001, pp.109-116. (ps-file) (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.85-99.

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, 25-28, 2000, St. Petersburg, Russia - Abstracts, pp.37-38. in Russian (with V.P.Shapeev)

1999

One class of partially invariant solutions of the Navier-Stokes equations.
Journal of applied mechanics and technical physics. 1999, 40, 2, pp.24-33. (ps-file) (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.337-343. (PDF-file) (with Yu.N.Grigoriev, P.Sattayatham)

An application of the differential constraints method for the two-dimensional equations of gas dynamics.
Prikl. matem. and mech., 1999, 63, 6, pp.909-916. (English transl. in J.Appl.Maths Mechs, 1999, v.63, 6. pp.885-891) (PDF-file) (with V.P.Shapeev)

1998

Group analysis of the Boltzmann equations of a relaxative multicomponent gas.
Dokl. Acad. Nauk Russia, 1998, 360 (4). (ps-file) (with Yu.N.Grigoriev)

Bobylev-Krook-Wu Modes for Multicomponent Gas Mixtures.
Physical Review Letters, 1998, v.81 (1), pp.93-95 (PDF-file) (with Yu.N.Grigoriev)

Group classification of two-dimensional stable viscous gas equations.
International Journal of Non-Linear Mechanics, 1998, v.34, 3, pp.449-456.

Symmetry and multiple waves in gas dynamics.
Lecture notes of the joint ISAMM/FRD inter-disciplinary Workshop on Symmetry analysis and mathematical modeling. International Institute for Symmetry Analysis and Mathematical Modeling at University of North-West (South Africa). 1998.

Application of group analysis in gas kinetics.
Lecture notes of the joint ISAMM/FRD inter-disciplinary Workshop on Symmetry analysis and mathematical modeling. International Institute for Symmetry Analysis and Mathematical Modeling at University of North-West (South Africa). 1998. (ps-file)

1997

Steady spatial non-isentropic double-wave type gas flows.
Prikl. Matemat. i Mekhanika. 1997, 61, 1. pp.159-167. (English transl. in J.Appl.Maths Mechs, 1997, v.61 (1).)

Group classification of three-wave equations in nonlinear optics.
International Conference on Modern Group Analysis (MOGRAN YII), Developments in Theory, Computation and Application, Nordfjord, (Norway), MARS Publishers, 1997. pp.219-226. (ps-file) (with A.V.Gorchakov)

Application of Group Analysis to the Boltzmann equation.
Proceedings of International conference on Computational Mathematics (ICCM'97), Bangkok. pp.189-194. (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 (1-2). pp.170-174. (PDF-file)

Group classification gas dynamics equations with constant body forces.
Journal of applied mechanics and technical physics. 1996, 1. (ps-file)

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.125-128. (ps-file) (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.139-144. (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.43-44. (with Yu.N.Grigoriev)

An application of the method of differential constraints to two-dimensional gas dynamics equations.
International Conference on the Methods of Aerophysical Research, ICMAR, Proceedings, Part 3, 1996, pp.221-226. (with V.P.Shapeev)

An application of the method of differential constraints to two-dimensional gas dynamics equations.
International conference "Mathematical models and numerical methods of continuum mechanics", 1996, Novosibirsk. pp.78-79. (with V.P.Shapeev)

1995

On double waves of equations with three independent variables.
Dokl. AS Russian, 1995, 345, 6. (ps-file)

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.172-178. (with Yu.N.Grigoriev)

Calculation of symmetry groups for integro-differential equations.
CRC Handbook of Lie Group Analysis of Differential Equations vol. 3, New Trends, 1995. pp.139-145. (with N.H.Ibragimov)

Differential constraints.
CRC Handbook of Lie Group Analysis of Differential Equations vol. 3, New Trends, 1995. pp.283-289. (with N.H.Ibragimov)

1994

Homogeneous autonomous systems with three independent variables.
Prikl. matem. and mech., 1994, 58, 5. pp.97-102. (English transl. in J.Appl.Maths Mechs, 1994, v.58, No.5, pp.857-863.). (ps-file)

Group classification of the two-dimensional gas dynamics equations.
Prikl. matem. and mech., 1994, 58, 4. pp.56-62. (English transl. in J.Appl.Maths Mechs, 1994, v.58, No.4, pp.629-635.) (ps-file)

One class of partial invariant solutions of plane gas flows.
Differential equations, 1994, 30, 10. (ps-file)

Reduction of double waves of homogeneous autonomous systems.
Seminar on analytic methods of gas dynamics and optimization SAMGOP-94. 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.57-58.

1993

Methods for constructing exact solutions of continuum mechanics equations.
Textbook, Novosibirsk state university, 1993. (ps-file)

Application of REDUCE system for analysis of compatibility of partial differential equations.
Modelirovanie v mechanike, Novosibirsk, 1993, 7(24), 4. pp.26-35. (with V.G.Ganzha, Shapeev V.P.)

Influence of rarefaction on mass transfer in a plasma-chemical reactor.
Computational technologies, 1993, v.2, 7. pp.47-54. (with Yu.N.Grigoriev)

1992

Influence of mass transfer on homogeneity in a planar reactor.
Surface, 1992, 12. pp.60-68. (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.89-95. (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.82-88.

On double-wave-type plane gas flows.
Russian Journal of Theoretical and Applied Mechanics, v.1, No.1, 1991, pp.47-54.

Group theoretical analysis of some kinetic equations.
Modelirovanie v mechanike, Novosibirsk, 1991, 5(22), 3. pp.27-39. (with Yu.N.Grigoriev)

Influence of rarefaction on mass transfer in a plasma-chemical 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 Ins-t of Heat Physics AS Ukrainian SSR, No.-90-84P, Kiev, 1991. (with V.G.Ganzha, S.S.Moskaluk, V.P.Shapeev, V.P.Shelest)

Page Last Updated 22 June, 2002