EqWorld Web Site

EqWorld

The World of Mathematical Equations

 IPM Web Site
Alexander V. Aksenov   

Alexander V. Aksenov

Ph.D., D.Sc., Professor

Born: 7 January 1953

Education and Degrees:

  • M.Sc., 1975, Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University;
  • Ph.D., 1982, Lomonosov Moscow State University;
  • D.Sc., 2005, Lomonosov Moscow State University.

Current Professional Status:

  • Professor, Lomonosov Moscow State University.

Membership:

Areas of Expertise:

  • exact solutions of nonlinear partial differential equations;
  • group analysis;
  • nonlinear problems of mathematical physics;
  • asymptotic methods;
  • partial differential equations for scientists and engineers;
  • hydrodynamics and gas dynamics.

Author:

  • More than 100 research papers.

Selected Publications:

  • Aksenov A.V., Kirillov V.P., Mozhaev V.V., Skorovarov V.E., Sheronov A.A. Structure of internal waves in a channel. Fluid Dynamics. 1985. V. 20. No. 1. Pp. 92-96.
  • Aksenov A.V., Mozhaev V.V., Skorovarov V.E., Sheronov A.A. Internal wave structure in a three-layer fluid with a stratified middle layer. Fluid Dynamics. 1987. V. 22. No. 3. Pp. 437-441.
  • Aksenov A.V., Mozhaev V.V., Skorovarov V.E., Sheronov A.A. Phase structure of three-dimensional internal waves in a channel. Fluid Dynamics. 1989. V. 24. No. 1. Pp. 107-113.
  • Aksenov A.V., Mozhaev V.V., Skorovarov V.E., Sheronov A.A. Stratified flow over a cylinder at low values of the internal Froude number. Fluid Dynamics.1989. V. 24. No. 4. Pp. 639-642.
  • Aksenov A.V., Samarov K.L. Lorentz-invariant solutions of pseudodifferential Schrodinger equation. Differential Equations. 1990. V. 26. No. 2. Pp. 204-207.
  • Aksenov A.V. Symmetries of linear partial differemtial equations and fundamental solutions. Doklady Mathematics. 1995. V. 51. No. 3. Pp. 329-331.
  • Aksenov A.V. Symmetries and invariant solutions of absolutely unstable media equations. Physics of Atomic Nuclei. 2000. V. 63. No. 4. Pp. 677-679.
  • Aksenov A.V. Symmetries and relations between solutions of the class Euler-Poisson-Darboux equations. Doklady Mathematics. 2001. V. 64. No. 3. Pp. 421-424.
  • Aksenov A.V. Linear differential relations between solutions of a class of Euler-Poisson-Darboux equations. Differential Equations. 2005. V. 41. No. 6. Pp. 824-832.
  • Aksenov A.V., Petrov A.G., Shunderyuk M.M. The motion of solid particles in a fluid in a nonlinear ultrasonic standing wave. Doklady Physics. 2011. V. 56. No. 7. Pp. 379-384.
  • Aksenov A.V. Nonlinear evolution of periodic gas perturbations. Bulletin of the Russian Academy of Sciences: Physics. 2011. V. 75. No. 1. Pp. 126-130.
  • Aksenov A.V., Kozyrev A.A. Reductions of stationary boundary layer equation. Ufa Mathematical Journal. 2012. V. 4. No. 4. Pp. 3-12.
  • Aksenov A.V. Nonlinear periodic waves in a gas. Fluid Dynamics. 2012. V. 47. No. 5. Pp. 636-646.
  • Aksenov A.V., Kozyrev A.A. Reductions of the stationary boundary layer equation with a pressure gradient. Doklady Mathematics. 2013. V. 87. No. 2. Pp. 236-239.
  • Aksenov A.V. Fundamental Solution of displacement equations for a transversely isotropic elastic medium. Doklady Mathematics. 2016. V. 94. No. 2. Pp. 598-601.
  • Aksenov A.V., Druzhkov K.P. Symmetries and reductions of Burgers-Huxley equation. Journal of Physics: Conference Series. 2017. V. 788. Pp. 1-6.
  • Aksenov A.V., Sudarikova A.D., Chicherin I.S. The surface tension effect on viscous liquid spreading along a superhydrophobic surface. Journal of Physics: Conference Series. 2017. V. 788. Pp. 1-6.
  • Aksenov A.V. Fundamental solution of the elasticity theory equations in displacements for a transversely isotropic medium. Differential Equations. 2017. V. 53. No. 5. Pp. 617-622.
  • Aksenov A.V. Method of construction of the Riemann function for a second-order hyperbolic equation. Journal of Physics: Conference Series. 2017. V. 937. No. 012001. Pp. 1-7.
  • Aksenov A.V. Symmetries of fundamental solutions and their application in continuum mechanics. Proceedings of the Steklov Institute of Mathematics. 2018. V. 300. Pp. 1-12.
  • Aksenov A.V., Dobrokhotov S.Yu, Druzhkov K. P. Exact step-like solutions of one-dimensional shallow-water equations over a sloping bottom. Mathematical Notes. 2018. V. 104. No. 6. Pp. 915-921.
  • Aksenov A.V. Symmetries and fundamental solutions of displacement equations for a transversely isotropic elastic medium . In: Modern Mathematics and Mechanics. Fundamentals, Problems and Challenges. Editors: Prof. Victor A. Sadovnichiy, Prof. Dr. Michael Z. Zgurovsky. Springer. 2019. Pp. 125-135.
  • Aksenov A.V. Asymptotics of an integral of a function of boundary layer type. Moscow University Mathematics Bulletin. 2019. V. 74. No. 5. Pp. 212-214.
  • Aksenov A.V., Chicherina A.D., Chicherin I.S. Self-similar solution for power-law liquid flow down an inclined plane. Journal of Physics: Conference Series. 2019. V. 1205. No. 012003. Pp. 1-5.
  • Aksenov A.V., Druzhkov K.P. Symmetries of the equations of two-dimensional shallow water over a rough bottom. Journal of Physics: Conference Series. 2019. V. 1205. No. 012002. Pp. 1-7.
  • Aksenov A.V., Druzhkov K.P. Contact symmetries and conservation laws of the first order of the equation of one-dimensional shallow water over a rough bottom in Lagrange's variables. Journal of Physics: Conference Series. 2019. V. 1392. No. 012001. Pp. 1-6.
  • Aksenov A.V., Druzhkov K.P. Group classification of the system of equations of two-dimensional shallow water over uneven bottom. Russian Journal of Mathematical Physics. 2020. V. 27. No 3. Pp. 277-298.
  • Aksenov A.V., Druzhkov K.P. Conservation laws of the equation of one-dimensional shallow water over uneven bottom in Lagrange's variables. International Journal of Non-Linear Mechanics. 2020. V. 119. No. 103348. Pp. 1-8.
  • Aksenov A.V., Druzhkov K.P. Symmetries and conservation laws of the equations of two-dimensional shallow water over uneven bottom. In: Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics. Understanding Complex Systems. Editors: Prof. Victor A. Sadovnichiy, Prof. Dr. Michael Z. Zgurovsky. Springer. 2021. Chapter 4.7. Pp. 113-163.
  • A. V. Aksenov, A. D. Polyanin. Methods for constructing complex solutions of nonlinear PDEs using simpler solutions, Mathematics, 2021, Vol. 9, No. 4, 345; doi:10.3390/math9040345
  • A. V. Aksenov, A. A. Kozyrev. New reductions of the unsteady axisymmetric boundary layer equation to ODEs and simpler PDEs, Mathematics, 2022, Vol. 10, No. 10, 1673; doi:10.3390/math10101673
  • A. V. Aksenov, A. A. Kozyrev. Group classification of the unsteady axisymmetric boundary layer equation, Mathematics, 2024, Vol. 12, No. 7, 988; 10.3390/math12070988
  • A. D. Polyanin, A. V. Aksenov, Unsteady magnetohydrodynamics PDE of Monge-Ampère type: Symmetries, closed-form solutions, and reductions, Mathematics, 2024, Vol. 12, No. 13, 2127; doi:10.3390/math12132127

Mailing Address:

Lomonosov Moscow State University,
1 Leninskie Gory, Main Building,
119991 Moscow, Russia

E-mail: aksenov@mech.math.msu.su
Page last updated: July 7, 2024 Main page of the EqWorld website