Sergey V. Meleshko, Ph.D., Dr.S.

Professor, Dr. Sergey V. Meleshko

Complete List of Publications

• 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) (ps-file) (with N.Manganaro) in press
• A particular class of partially invariant solutions of the Navier-Stokes equations.
  European J. of Applied Mathematics (sent) (ps-file)
• 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)

• 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)

• 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. (ps-file)
• 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)

• 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)

• 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. (PDF-file)
• 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. (ps-file)
• 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)

• 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).) (PDF-file)
• 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)

• 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)

• 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)

• 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.

• 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)

• 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)

• 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)

• On potential polytropic gas flows of triple waves.
  Prikl. matem. and mech., 1990, 54, 5. pp.775-779. (English transl. in J.Appl.Maths Mechs, 1990, v.54, No.5.)
• Double waves in ideal rigid-plastic body with a plane deformation.
  Journ.prikl.mech.i techn.phyz, 1990, 2. pp.131-136.
• Group theoretical analysis of the kinetic Boltzmann equation and its models.
  Arch. Mech., 1990, v.42, No.6, pp.693-701. (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)

• On nonisoentropic steady space and plane unsteady double waves.
  Prikl. matem. and mech., 1989, 53, 2. pp.255-260. (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.49-58. (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)

• On plane flows of a double wave type.
  Modelirovanie v mechanike, Novosibirsk, 1988, 2(19), 2. pp.111-118.
• On group properties of viscoelastic media motion equations.
  Modelirovanie v mechanike, Novosibirsk, 1988, 2(19), 4. pp.116-126.
• 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.107-115. (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.45-52. (with Yu.N.Grigoriev, A.N.Mikhalicyn)

• Group analysis of the integro-differential Boltzmann equation.
  Dokl. Acad. Nauk S.S.S.R., 1987, 297, 2. pp.323-327. (with Yu.N.Grigoriev)

• 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.115-123.
• An analytical and numerical study of compressible flows based on the parabolized Navier-Stokes equations.
  The IY international conference on boundary and interior layers (BAIL-IY). 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, 18-86. 51 pp. (with Yu.N.Grigoriev)
• An application of differential constraints method for description of wave propagation in elastic-viscoplastic medium.
  Sixth national meeting on theoretical and applied mechanics. Abstracts and presentations, 1986. p.450. (with V.P.Shapeev)

• A classification of a plane isentropic gas flow of a double wave type.
  Prikl. matem. and mech., 1985, 49, 3. pp.406-410. (English transl. in J.Appl.Maths Mechs, 1985, v.49, No.3.)
• Invariant solutions of the parabolized Navier-Stokes compressible gas equations.
  Theoretical and applied problems of the computational mathematics and mathematical physics. Riga. 1985, pp.173-174.
• An investigation of viscous compressible flows based on the parabolized Navier-Stokes equations.
  Preprint of Institute of Theoretical and Applied Mechanics, 1985, 32-85. 47 pp. (with S.G.Cherny)

• A stress wave propagation of a simple wave type in an elastic-viscoplastic media.
  Chisl. meth. resh. zadach of the theory of elastic and plastic. Novosibirsk. 1984, pp.205-211.
• Method of differential constraints.
  Physical mechanics of inhomogeneous media. Novosibirsk. 1984, pp.3-13. (with V.P.Shapeev, N.N.Yanenko)

• Differential constraints and one-parameter Lie-Backlund transformation groups.
  Dokl. AS USSR, 1983, 271, 1. pp.42-46; (English transl., Soviet Math. Dokl., 28, 37-41).
• About jointing of DP-solutions over strong discontinuity.
  Chisl.metody and the problem of optimization, Tomsk, 1983, pp.15-23. (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.125-131. (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.314-329. (with V.G.Ganzha, S.I.Mazuric, V.P.Shapeev, N.N.Yanenko)

• Symbolic manipulations in methods for solving problems in mathematical physics.
  Symp. Mathematics for computer science. Paris. 1982. pp.431-438. (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.77-85. (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 20-82. pp.24-25. (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.123-129. (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)

• 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.87-100.
• Realization on computer an algorithm for studying consistency of systems of partial differential equations.
  Dokl. AS USSR, 1981, 261, 5. pp.1044-1046. (with V.G.Ganzha, F.A.Murzin, V.P.Shapeev, N.N.Yanenko)

• DP-conditions and a joining problem of different DP-solutions.
  Chisl.metody mech.splosh. sredy, Novosibirsk, 1980, 11, 6. pp.96-109.
• Method of differential constraints and a problem of decay an arbitrary discontinuity.
  Preprint of Institute of Theoretical and applied mechanics, 1980, No. 47, pp.24-25.
• Method of differential constraints and a problem of decay an arbitrary discontinuity.
  Dokl. AS USSR, 1980, 254, 4, pp.796-798 (Soviet Math. Dokl., 1980, 22, 2, pp.447-449.) (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.109-117. (with V.P.Shapeev)

• An application of DP-solutions to the problem of decay an arbitrary discontinuity in inelastic continuous media.
  Chisl.metody mech.splosh.sredy, Novosibirsk, 1979, 10, 6. pp.85-96. (with V.P.Shapeev)

• One method of defining a state equation.
  Chisl.metody mech.splosh.sredy, Novosibirsk, 1977, 8, 1. pp.83-87. (with V.P.Shapeev)