Vladimir N. Grebenev

Address in Russia Federal Research Center for

Information and Computational Technologies

Siberian Division of Russian Academy of Sciences(SDRAS) Laboratory of Mathematical Modeling

Ac. Lavrentjev Ave. 6

630090 Akademgorodok, Novosibirsk, Russia

Telephone + 7 383 330 85 70 (in Russia)

Cell Phone + 7 905 936 15 72 (in Russia)

E-mail vngreb[email protected]

Education / Academic Degrees

    2005 Doctor of Science Degree in Differential Equations (corresponds to habilitation), High Certification Commission of the Russian Fed- eration, Moscow, Russia

    1987 Ph.D. in Physics and Mathematical Sciences, Novosibirsk State University, Russia

    1979 Diploma in Math. and Applied. Math., Novosibirsk State Univer- sity (Equivalent to Masters Degree), Russia

    1988 - 1991 Institute of Theor. Appl. Mech. (Russ. Acad. Science), Novosi- birsk Researcher of Laboratorrnal of Physics A Highlights of 2017 collection, UK

Institute of Mathematics and Statistics, Brazil

10/2015 - 12/2015 Fund of Engineering and Physics Research Council, UK for short- term visit

· The University of Warwick, Mathematical Institutes, UK

06/2015 - 07/2016 Fund of Engineering and Physics Research Council, UK for short- term visit

· The University of Warwick,Mathematical Institutes, UK

09/2017 - 12/2017 DAAD (Research Stays for University Academics and Scientists)

· Darmstadt Technical University, Germany

Fachgebiet für Str?mungsdynamik (FDY) Fachbereich Maschi- nenbau Technische Universit?t Darmstadt

10/2018 - 11/2018 CNRS (Centre National de la Rechercher Scienti?que, Fédération Wolfgang DOEBLIN)

· The University of Nice, France

11/2018 - 12/2018 · Darmstadt Technical University, Germany

Fachgebiet für Str?mungsdynamik (FDY) Fachbereich Maschi- nenbau Technische Universit?t Darmstadt

02/2019 - 08/2019 Grant of FAPESP (grant no. 2018/21330-2)(Science Foundation of Sao Paulo State, Brazil) for short-term visit

· Sao Paulo University,

Institute of Mathematics and Statistics, Brazil

03/2020 - 03/2020 CNRS (Centre National de la Rechercher Scienti?que, Fédération 11/2020 - 12/2020

Wolfgang DOEBLIN)

· The Institut de Physique de Nice, Universite Cote D’Azur, France

10/2021 - 04/2022 Grant of FAPESP (grant no. 2021/09845-0)(Science Foundation of Sao Paulo State, Brazil) for short-term visit

· Sao Paulo University,

Institute of Mathematics and Statistics, Brazil

10/2022 - 04/2023 Grant of FAPESP (grant no. 2021/09845-0)(Science Foundation of Sao Paulo State, Brazil) for short-term visit

· Sao Paulo University,

Institute of Mathematics and Statistics, Brazil

03/2024 - 05/2024 · Darmstadt Technical University, Germany

Fachgebiet für Str?mungsdynamik (FDY) Fachbereich Maschi- nenbau Technische Universit?t Darmstadt

10/2024 - 12/2024 · Sino-Russian Mathematical Center

Peking University, National Key R D Program of China

2020YFE0204200 and Sino-Russian Mathematical Center, Op- tical wave turbulence: Lie algebra of the conformal symmetry transformations of quantum ?uids of light, Gauge group.

Individual Invitations for Research Collaboration

Guest Scientists

· Prof. Launder (UMIST,UK). Common visit at Institute of Computational Technologies and Institute of Thermophysics SD RAS in the frame of INTAS project: Modeling non- local turbulent transport of momentum, heat and substance in strati?ed ?ows; 05/2002.

· Prof. Oberlack and Dr. Waclawczyk (Technical University Darmastadt,Germany). Visit at Institute of Computational Technologies SD RAS in the frame of the Third German- Russian Week of the Young Researcher: Aviation and Space; 09/2013.

· Prof. Nazarenko (Mathematical Institute, University of Warwick, UK). Visit at Institute of Computational Technologies; 10/2012 - 11/2012; 04/2013 - 06/2013.

· Prof. Nazarenko (INSTITUT de PHYSIQUE de NICE, France). Visit at Institute of Computational Technologies and Novosibirsk State University; 07/2019 - 08/2019.

Review Activities

Governmental and Semi-Governmental Organizations

· Reviewer for Mathematical Reviews

· Reviewer for Zentralblatt fur Matematik

· Reviewer for Expert Community in Science and Engineering Fields of Ministry of Science and Technologies of Russian Federation

Dissertations Inland

Reviewer more than 15 dissertations International Journals

· Computational Applied Mathematics

· Physics of Combustion and Explosion

· Journal of Computational Technologies

· Siberian Journal of Industrial Mathematics

· Fluid Dynamics Research

· European Journal of Applied Mathematics

· Journal of Nonlinear Mathematical Physics

· Journal of Fluid Mechanics

· Journal of Turbulence

Publishing Houses

· Science (Moscow, Novosibirsk)

Association Memberships

· The American Mathematical Society (AMS)

· European Mathematical Society (EMS) Publications

Scienti?c Quali?cation

[1] Stationary solutions of a forward-backward parabolic equation arising in turbulence (in Russian), Master Thesis, Novosibirsk State Univer. , (1979)

[2] Solvability of non-classical initial-boundary value problems for a forward-backward parabolic equation (in Russian), Dissertation, Novosibirsk State Univer. , (1987)

[3] Level-set method: the application to free boundary problems arising in turbulence and porous medium (in Russian), Habilitation Thesis, Novosibirsk State Univer. , (2005)

Books and Refereed Archival Journals

[4] Grebenev V.N. Optical Wave Turbulence: The Conformal Symmetry Transformations of Statistics of the Quantum Fluids of Light. CSIAM Trans. Appl. Math. DOI: 10.4208/csiam-am.SO-2024-0061 Publication Date : 2025-06-30.

[5] Grebenev V.N., Grishkov A.N. Generalized Brenier Principle and the Closure Problem of Landgren–Monin–Novikov Hierarchy for Vorticity Field. Doklady Physics. - 2024. Vol.515(2). -P. 43–50.

[6] Grebenev V.N., Demenkov A.G., Chernykh G.G. Local Equilibrium Approach in the Problem of the Dynamics of a Plane Turbulent Wake in a Passively Strati?ed Medium. Journal of Applied and Industrial Mathematics. - 2024. - Vol.18. - P.36-46. - ISSN 1990-4789. - EISSN 1990-4797.

[7] Grebenev V.N., Demenkov A.G., Chernykh G.G. Investigation of the Local Equi- librium Approximation in a Planar Momentumless Turbulent Wake in a Passively Strati?ed Fluid. Journal of Engineering Thermophysics. - 2024. - Vol.33. - Iss. 3. - P.494-506. - ISSN 1810-2328. - EISSN 1990-5432

[8] Grebenev V.N., Grishkov A.N. Towards Finding the Conformal Invariance of the Multi-point Vorticity Statistics in 2d Turbulence. Journal of Vibration Testing and System Dynamics. - 2024. - ISSN 2475-4811. - EISSN 2475-482X.

[9] Grebenev V.N., Grishkov A.N. A Gauge-Invariant Lagrangian Determined by the n- Point Probability Density Function of a Vorticity Field of Wave Optical Turbulence. Doklady Physics. - 2023. - Vol.68. - Iss. 12. - P.416-421. - ISSN 1028-3358. - EISSN 1562-6903.

[10] with A. Grishkov, S. Medvedev: Symmetry transformations of statistics of the vorticity ?eld in optical turbulence. J. Theor. Math. Phys. , . - 2023. - Vol.217. - Iss. 2. - P.1795-1805. - ISSN 0040-5779. - EISSN 1573-9333.

[11] with A.G. Demenkov, G.G. Chernykh: Local equilibrium approximation in the prob- lem of dynamics of the far plane turbulent wake in the passive strati?ed medium. Siberian J. Industrial Mathematics , 4 accepted (2023).

[12] with A. Grishkov, M. Oberlack: Symmetry of the Lundgren–Monin–Novikov equation for the probability distribution of the vortex ?eld. Doklady Physics, 68 , pp. 42–47. (2023)

[13] with A. Grishkov, S. Medvedev, M. Fedoruk: Hydrodynamic approximation for two- dimensional optical turbulence: symmetries of statistical distributions. Quantum elec- tronics 52:11, 1023–1030 (2022)

[14] with A.G. Demenkov, G.G. Chernykh: Local equilibrium approximation in the mathe- matical model of the far turbulent wake behind a body of revolution. J. Appl. Mechan. Techn. Phys. 63:5, 825–832 (2022).

[15] with A. Grishkov, SLE: di?erential invariants study. Sao Paulo J. Math. Sci. doi.org/10.1007/s40863-022-00299-8 (2022)

[16] with S. Thalabard, S. Medvedev, S. Nazarenko: Inverse cascade anomalies in fourth- order Leith models. J. Phys A: Math. Theor. Vol.55(1) (2022)

[17] with D.O. Bykov, S.B. Medvedev: Hamiltonian Structure and Conservation Laws of Three-Dimensional Linear Elasticity Theory (P.99-123). Chapter in book: Luo A.C.J., Gazizov R.K. (eds) Symmetries and Applications of Di?erential Equations. Nonlinear Physical Science. Singapore: Springer. ISBN 978-981-16-4682-9: (2021)

[18] with M. Wac?awczyk, M. Oberlack: Conformal invariance of the 1-point statistics of the zero-isolines of 2d scalar ?elds in inverse turbulent cascades. Physical Review Fluids 6(084610): (2021)

[19] with B. Semisalov, S. Medvedev, S. Nazarenko: Numerical analysis of a self-similar turbulent ?ow in Bose – Einstein condensates. Communications in Nonlinear Science and Numerical Simulation 102(105903): (2021)

[20] with A. Demenkov, G. Chernykh: METHOD OF DIFFERENTIAL CONSTRAINTS: LOCAL EQUILIBRIUM APPROXIMATION IN A PLANAR MOMENTUMLESS TURBULENT WAKE. J. Appl. Mechan. Techn. Phys. 62(3), 383–390: (2021)

[21] with A.N. Grichkov, M. Oberlack, M. Wac?awczyk: Second-order invariants of the in- viscid Lundgren–Monin–Novikov equations for 2d vorticity ?elds. Zeitschrift fur ange-

wandte Mathematik und Physik ZAMP 72(3): (2021) https://doi.org/10.1007/s00033- 021-01562-2

[22] with A.N. Grichkov, A.G. Demenkov, G.G. Chernykh: Local equilibrium ap- proximation in free turbulent ?ows: Veri?cation through the method of di?er- ential constrains. Zeitschrift fur angewandte Mathematik und Mechanik ZAMM https://doi.org/10.1002/zamm.202000095: (2021)

[23] with M. Wac?awczyk, M. Oberlack: Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models. Symmetry MDPI 12(1482):1–19 (2020)

[24] with S.V. Nazarenko, S.B. Medvedev, B Semisalov: Steady states in dual-cascade wave turbulence. J. Phys A: Math. Theor. Vol.53(36) (2020)

[25] with M. Wac?awczyk, M. Oberlack: Conformal invariance of the zero-vorticity La- grangian path in 2D turbulence. J. Phys. A: Math. Theor. Vol. 52(33) (2019)

[26] with S.V. Nazarenko, S.B. Medvedev, S Galtier: The focusing problem for the Leith model of turbulence: a self-similar solution of the third kind. J. Phys A: Math. Theor. Vol.52(15) (2019)

[27] with M. Oberlack, M. Wac?awczyk : Statistical symmetries of turbulence. Chapter In book: Nonlinear Systems and Their Remarkable Mathematical Structures: Volume I 1st Edition Norbert Euler Publisher: CRC Press Published December 3, 2018

[28] with M. Oberlack : Homogeneous Isotropic Turbulence: geometric and isometry prop- erties of the 2-point velocity correlation tensor J. Nonl. Math. Phys, Vol. 25, N4, (2018)

[29] with N.K Bell, S.B. Medvedev, S.V. Nazarenko In: Highlights. A collection of out- standing research published in 2017. Fluid and plasma theory. Special Issue Journal of Physics A: Mathematical and Theoretical ISSN 1751-8113. - EISSN 1751-8121 (2018)

[30] with M. Wac?awczyk, M. Oberlack : Conformal invariance of the Lungren-Monin- Novikov equations for vorticity ?elds in 2D turbulence. J. Phys. A: Math. Theor. Vol. 50(43) (2017) 435502

[31] with N.K Bell, S.B. Medvedev, S.V. Nazarenko : Self-similar evolution of Alfven wave turbulence. J. Phys A: Math. Theor. Vol.50(43) (2017) 435501

[32] with A. Gri?n, S.B. Medvedev, S.V. Nazarenko In: Highlights. A collection of out- standing research published in 2016. Fluid and plasma theory. Special Issue Journal of Physics A: Mathematical and Theoretical ISSN 1751-8113. - EISSN 1751-8121 (2017)

[33] with M. Waclawczyk, M. Oberlack: Lie symmetry analysis of the Lundgren-Monin- Novikov equations for multi-point probability density functions of turbulent ?ow. Phys. A: Math. Theor. Vol. 50(17) (2017) 175501 doi.org/10.1088/1751-8121/aa62f4

[34] with S.V. Nazarenko, S.B. Medvedev : Complementary remarks to properties of the energy spectrum in Leith’s model of turbulence. ZAMM Z. Angew. Math. Mech., (in press) (2017).

[35] with S.V. Nazarenko: Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence. Phys. A: Math. Theor. Vol. 50(3), (2017) http://dx.doi.org/10.1088/1751-8121/50/3/035501

[36] with M. Oberlack, A.G. Megrabov, A.N. Grishkov: Symmetry transformations of an ideal steady ?uid ?ow determined by a vector potential. J. Math. Phys. Vol. 57(10), 103506 (2016); http://dx.doi.org/10.1063/1.496522420016

[37] with A. Gri?n, S.B. Medvedev, S.V. Nazarenko: Steady states in the Leith’s model of turbulence. Phys. A: Math. Theor. Vol. 49(36), (2016).

[38] with S.B. Medvedev: Hamiltonian structure and conservation laws of two- dimensional linear elasticity theory. ZAMM, Z. Angew. Math. Mech., DOI 10.1002/zamm201500090 (2016).

[39] with S.V. Nazarenko, S.B. Medvedev, I.V. Schwab and Yu.A. Chirkunov In: High- lights. A collection of outstanding research published in 2014. Fluid and plasma theory, p.40. Special Issue Journal of Physics A: Mathematical and Theoretical ISSN 1751-8113. - EISSN 1751-8121 (2015).

[40] with S.V. Nazarenko, S.B. Medvedev, I.V. Schwab and Yu.A. Chirkunov: Self-similar solution in Leith model of turbulence: anomalous power law and asymptotic analysis. Phys. A: Math. Theor. Vol. 47(2) 025401 (2014).

[41] with M. Frewer and M. Oberlack: The dual stream function representation of an ideal steady ?uid ?ow and its local geometric structure. Math. Phys. Anal. Geom. Vol. 17(1-2), pp. 3-25, (2014) DOI: 10.1007/s11040-014-9138-5.

[42] with Yu. A. Chirkunov, S. V. Nazarenko, S. B. Medvedev. Invariant solutions for the nonlinear di?usion model of turbulence. Phys A: Math. Theor. Vol. 47, No.18. 185501, (2014) DOI: 10.1088/1751-8113/47/18/185501

[43] with S.V. Nazarenko, I.V. Schwab, Yu.A.Chirkunov, G.G. Lazareva, S.B. Medvedev. Self-similar solution of a nonlinear di?usion equation for the spectral density energy of turbulence. J. Computational Technologies Vol. 19(1), pp. 63-73, (2014)

[44] with A.N. Grishkov and M. Oberlack: The extended symmetry Lie algebra and the asymptotic expansion of the transversal correlation function for isotropic turbulence, Adv. Math. Phys. , Vol 2013, article ID 46954, 11 pp., (2013) http://dx.doi.org/10.1155/2013/469654

[45] with M. Oberlack and A.N. Grishkov: In?nite dimensional Lie algebra associated with the two-point velocity correlation tensor from isotropic turbulence, ZAMP, Z. Angew. Math. Phys., Vol 64, pp. 599–620, (2013) DOI: 10.1007/s00033-012-0251-7

[46] with M. Oberlack: A geometry of the correlation space and a nonlocal degenerate parabolic equation from isotropic turbulence. ZAMM, Z. Angew. Math. Mech. Vol 92, N3, pp. 179–195, (2012)

[47] with S.B. Medvedev: Homogeneous isotropic turbulence: geometry and admitted groups of transformations J. Comput. Tech. , Vol. 17, N5, pp. 23–45, (2012) (in Russian)

[48] with M. Oberlack: Geometric realization of the two-point velocity correlation tensor for isotropic turbulence, J. Nonl. Math. Phys. , Vol 18, N1, pp.109 –120 (2011), doi: 10.1142/S1402925111001192

[49] Degeneracy of homogeneous isotropic turbulence in the limit of large Reynolds num-

bers J. Comput. Tech. , Vol. 16, N5, pp. 16–29, (2011) (in Russian)

[50] with M. Oberlack, Shi-Jun Liao and Zeng Liu: Explicit series solution of a closure model for the von Kármán-Howarth equation, J. ANZIAM, Vol 52, N2, pp. 179–202, (2010)

[51] with M. Filimonov: Conservation of the Loitsyansky invariant in the Millionshtchikov model of homogeneous isotropic turbulence Vestnik NSU, Vol. 4, pp. 23-37, (2009) (in Russian)

[52] with M. Oberlack: A geometric interpretation of the second-order structure function arising in turbulence Math. Phys. Anal. Geom. , Vol 12, N1, pp. 1–18, (2009)

[53] with M. Oberlack, A. Grishkov : Lie algebra methods for the application to the statistical theory of turbulence J. Nonl. Math. Phys, Vol. 15, N2, pp. 227-251, (2008)

[54] with A. Grishkov, M. Oberlack : Lie algebra methods in the statistical theory of turbulence IME USP (Inst. Math. Stat. Sao Paulo Univer.) Preprint RT-MAT 2007-1, pp.1-29, (2007)

[55] with M. Oberlack : Approximate Lie symmetries of the Navier-Stokes equations J. Nonl. Math. Phys, Vol. 14, N2, pp. 157-163, (2007)

[56] with M. Oberlack : Compatible di?erential constraints to an in?nite chain of transport equations for cumulants Comm. in Nonl. Sci. Numer. Simul. (doi:10.1016/j.cnsns.2005.03.003), Vol. 12, pp. 336-349, (2007)

[57] with M. Oberlack : Integration of in?nite chain of transport equations for cumulants PAMM., Vol. 6, pp. 519-520, (2006)

[58] with M. Oberlack : Hidden symmetries to a Hanjalic-Launder model of turbulence Regular and Chaotic Dynamics, Vol. 11 N3, pp. 371-381, (2006)

[59] with M. Oberlack : A Chorin-type formula for solutions to a closure model for the von Karman-Howarth equation J. Nonl. Math. Phys. , Vol. 12, N1, pp. 1-9, (2005)

[60] with G. Chernykh : Invariant manifolds in parametric models of turbulence Revista de Matematica: Teoria y Aplicaciones, Vol. 11, N2, pp. 51-72, (2004)

[61] with G. Chernykh : Analysis of locally equilibrium approximation in a momentumless turbulent wake Comput. Technol. , Vol. 8, N3, pp. 11-24, (2003)

[62] with A.G. Demenkov, G.G. Chernykh : Analysis of locally equilibrium approximations in the problem of a far plane wake dynamics Dokl. Russian Acad. Sci. Ser. Mech, Vol. 382, N1, pp. 57-60, (2002)

(English transl. Doklady Physics. 47, pp. 518-521, 2002)

[63] with B.B. Ilyushin : Invariant sets and explicit solutions to a third-order model for shearless strati?ed turbulent ?ows J. Nonl. Math. Phys. , Vol. 9, N2, pp. 1-13, (2002)

[64] with B.B. Ilyushin : The di?erential constraints method: application to analysis of shearless turbulence mixing layer PAMM. Proc. Appl. Math. Mech. , 2001. 1(1), P.426-427, (2001)

[65] Far a plane turbulent wake dynamics. II Russ. J. Numer. Anal. Math. Modelling

(VSP, Utrecht) , Vol.17, N2, pp.135-143, (2002)

[66] with B.B. Ilyushin : The di?erential constraints method in the problem of shearless strati?ed mixing layer Dokl. Russian Acad. Sci. Ser. Mech. , Vol. 382, N6, English transl. Doklady Physics. 45, pp. 550-554, (2002)

[67] Annual Report of Russian Acad. Science. Principal results at 2001 Section of Math. Modeling. Comput. and Applied Math., p.76, Moscow

[68] with B.B. Ilyushin: A method for analyzing turbulence models Revista de Matematica: Teoria y Aplicaciones ,Vol. 8, N2, pp.85-99, (2001)

[69] with B.B. Ilyushin, Yu.I. Shokin: The use of di?erential constraints for analyzing turbulence models Inter. J. Nonl. Sci. Numer. Simul. ,Vol.1, N4, pp. 305-317, (2000)

[70] with B.B. Ilyushin: Application of di?erential constraints for analyzing turbulence models Dokl. Russian Acad. Sci. Ser. Mech. ,Vol.374, N.6, pp. 371-375, (2000)

[71] with B.B. Ilyushin: On a class of selfsimilar solutions to the problem of a shearless mixing layer dynamics in turbulent ?ows Sib. J. Indust. Math, Vol. 2, N.2,pp. 51-59, (1999)

[72] with B.B. Ilyushin: Equipotential line method in nonlinear di?usion problems Russ. J. Numer. Anal. Math. Modeling, 14(4),pp.299-382, (1999)(VSP,Utrecht, Netherlands)

[73] Dinamica de una huella plana turbulenta alejada Revista de Matematica: Teoria y Aplicaciones, 5(1),pp.177-184, (1998)

[74] Sobre la convexidad de la funcion de presion en el problema de la ?ltracion no lineal Revista de Matematica: Teoria y Aplicaciones, 5(1),pp.1-10, (1998)

[75] On a problem of far plane turbulent wake dynamics Sib. J. Indust. Math. , Vol. 1, N.1,pp. 97-103, (1998)

[76] Heat propagation in a planar zero-momentum turbulent wake Comput. Math. Math. Phys., Vol.37, N.7, pp. 854-861, (1997)

[77] Interfacial phenomenon for one-dimensional equation of forward-backward parabolic type Annali di Matematica Pura ed Applicata, Vol. CLXXV, (IV), pp.379-394, (1996)

[78] Nonlinear problems in semi-empirical theory of turbulence Uspekhi Mat. Nauk, Vol.50, N.4, p. 89, (1995)

Advances in Math. (English transl.)

[79] On a system of degenerate parabolic equations which arises in hydrodynamics of free turbulent ?ows Sib. Math. J. , Vol. 35, N. 4,pp. 670-682, (1994)

printed in USA by Plenum Publ. Co.

[80] Di?usion of a turbulent layer in a problem with singular perturbed turbulent energy Sib. Math. J. , Vol. 32, N. 1, pp. 1745-1756, (1992)

[81] On a dynamical system arising in the problem of turbulent layer spreading in homo- geneous ?uid Comput. Math. Math. Phys. , Vol. 32, N. 1, pp.103-113, (1992)

[82] Transformation of coordinates in a problem with free boundariesSib. Math. Zh. ,

Vol.32, N.3, pp. 39-46, (1991)

[83] (English transl.by) Plenum Publ. Co., Sib. Math. J. , January, 32, N. 3 pp.383-389, (1991)

[84] Solvability of the problem of dynamics of turbulent layer in homogeneous ?uid Di?er- ential’nye Uravneniay, V.27, N. 10, pp.1725-1733, (1991)

by Consults Bureau NY, Di?er. Equations

[85] On solvability of the problem of development of a domain of turbulent burst in a homogeneous ?uid USSR Comput. Math. Math. Phys. , V.30, N.2, pp. 187-190, (1990)

[86] with Novikov V.A.: On an investigation of solutions to a nonlinear equation of variable type Uspekhi Mat. Nauk, N.2, p. 156, (1987)

(Russian). Soviet Advances in Math. (English transl.)

Refereed Symposia and Conference Contributions (selected)

[87] with M. Oberlack : Compatible di?erential constraints to an in?nite chain of transport equations for cumulants. Proc. of Wall- Bounded and Free-Surface Turbulence and its Computation. Simposium, Singapore, (2005)

[88] Invariant manifolds of semi-empirical models of turbulence Proceedings of the Inter- national Mathematical Congress, Beijing, China 2002, pp. 876-877 (2002)

[89] with B.B. Ilyushin: Algebraic parameterizations of triple correlations in modeling a shearless turbulence mixing layer Advances in Turbulence VIII, Editor C. Dopazo, Barcelona, Spain. Proceedings of the 8th European Conference in Turbulence , pp. 359-362, (27-30/06/2000)

[90] with B.B. Ilyushin: On a class of selfsimilar solutions for a third-order model of shear- less turbulence mixing layer 16th Imacs Worlds Congress 2000, Proceedings, Lausanne , No. 411-49,5, (21-25/08/2000)

Edited by: Michel Deville, Robert Owens. Dept. of Computer Science, Rutgers Uni- versity

[91] Some geometrical properties of solutions to porous medium equation Proceedings of 2nd Asian Mathematical Conference, Invited paper, Thailand, October, 17-20, 1995, 5(1),pp.333-343, (1998)

World Scienti?c, Singapore, 1997

[92] Well-posed problems for models of free turbulence Proceedings of 2nd Sibirean Congr.Appl. and Indust. Math., pp.250-251, (06/1996)Novosibirsk, Russia