Research Interests

- applied mathematics
- partial differential equations
- fluid dynamics
- upscaling
- homogenization theory
- nonlinear flows in porous media

RESEARCH STATEMENT


PUBLICATIONS

Journal Papers

  1. (with Eugenio Aulisa, Yalchin Efendiev and Akif Ibragimov)
    Upscaling of Nonlinear Forchheimer Flows, (arXiv preprint)
  2. (with Eugenio Aulisa and Akif Ibragimov)
    Time asymptotic of non-Darcy flows controlled by total flux on the boundary, J. Math. Sciences 184 (4) (2012), pp. 399-430   (.pdf)
  3. (with Eugenio Aulisa and Akif Ibragimov)
    Long-term dynamics for well productivity index for non-linear flows in porous media,
    J. Math. Phys. 52 (2) (2011), 26 pp, doi 10.1063/1.3536463   (.pdf)
  4. (with Eugenio Aulisa, Luan Hoang and Akif Ibragimov)
    Analysis of generalized Forchheimer flows of compressible fluids in porous media,
    J. Math. Phys. 50, 103102 (2009), 44 pp, doi 10.1063/1.3204977   (.pdf)
  5. (with I. Smirnov), Optimal boundary control by elastic force at one end and displacement at the other end for the string oscillation problem on arbitrary sufficiently large time interval, Differential Equations, 45 (6) (2009), 878-888   (.pdf)

Proceedings

  1. Optimal boundary control by elastic force at one end and displacement at other end for the string oscillation problem, Proceedings of the 14th Saratov winter school "Contemporary problems of the theory of functions and applications" dedicated to the memory of academician P.L.Ulyanov, 2008.
  2. Optimal boundary control by elastic force at one end and displacement at other end for the string oscillation problem on arbitrary sufficiently large time interval, Collected theses of the best diploma works, Department of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, p.35, 2007.
  3. Optimization of boundary control for wave equation on sufficiently large time interval, Materials of the XIV international scientific conference for undergraduate and graduate students and young scientists "Lomonosov", Lomonosov Moscow State University, Moscow, Russia, p.8, 2007.
  4. Generalized solution for the telegraph equation with the zero-initial conditions and the Neumann conditions, Materials of international conference "Contemporary problems of applied mathematics and mathematical modeling", Voronej, Russia, p.33, 2005.

PRESENTATIONS

Conference Talks

  1. Time asymptotics of non-Darcy flows controlled by total flux on the boundary, Session on Differential Equations and Numerical Methods, Joint Mathematics Meeting, San Diego, CA, USA, Jan. 11, 2013.
  2. Upscaling method for Forchheimer flow of the compressible and incompressible fluid in heterogeneous porous media, AMS Fall Western Sectional Meeting, Session on Geometrical Methods in Mechanical and Dynamical Systems, University of Arizona, Tucson, AZ, USA, Oct. 27, 2012.
  3. Modeling of well productivity index for non-linear flows and applications in reservoir engineering, SIAM Conference on Mathematical and Computational Issues in the Geosciences, Long Beach, CA, USA, March 21, 2011.
  4. Longterm dynamics for well productivity index for non-linear flows in porous media, AMS Fall Western Sectional Meeting, Session on Nonlinear Phenomena: Applications of PDEs to Fluid Flows, UCLA, Los Angeles, CA, USA, Oct. 10, 2010.
  5. Generalized Forchheimer flows in porous media and applications, Rocky Mountain Mathematics Consortium Summer School "Conservation Laws & Applications", University of Wyoming, Laramie, WY, USA, June 29, 2010.
  6. Mathematical modeling of the productivity index of the well for non-linear flows in porous media, SIAM 8th Annual Graduate Student Research Day, Texas Tech University, Lubbock, TX, USA, April 8, 2010.
  7. Mathematical model of well productivity index for generalized Forchheimer flows and applications, SIAM Conference on Mathematics for Industry: Challenges and Frontiers (MI09), SIAM, San Francisco, CA, Nov. 2009.
  8. Optimal boundary control for wave equation SIAM 7th Annual Graduate Student Research Day, Texas Tech University, Lubbock, TX, USA, March 26, 2009.
  9. Optimal boundary control by elastic force at one end and displacement at other end for the string oscillation problem, 14th Saratov winter school "Contemporary problems of the theory of functions and applications" dedicated to the memory of academician P.L.Ulyanov, Saratov, Russia, Jan. 2008.
  10. Optimization of boundary control for the wave equation on sufficiently large time interval, XIV international scientific conference of undergraduate and graduate students and young scientists "Lomonosov", Lomonosov Moscow State University, Moscow, Russia, April 12, 2007.

Poster Presentations

  1. Pseudo-steady state attractors for fully transient Forchheimer flows in porous media, SIAM Conference on Mathematical and Computational Issues in the Geosciences, Long Beach, CA, USA, March 21, 2011.
  2. New methods for modeling productivity index of the well for generalized Forchheimer flows in porous media, 9-th Annual Graduate Student Research Poster Competition, Texas Tech University, Lubbock, TX, USA, March 29, 2010.
  3. New methods for modeling productivity index of the well for generalized Forchheimer flows in porous media, InterPore 2010 Conference and Annual Meeting, Texas A&M University, College Station, TX, USA, March 15, 2010.

Seminar Talks

  1. Upscaling of non-Darcy flow, Applied Mathematics Seminar, Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, USA, Oct. 24, 2012.
  2. Upscaling of fine scale geological models for non-linear flow simulations, Department of Mathematics, Texas A&M University, College Station, TX, USA, Oct. 22, 2012.
  3. Time asymptotic of non-Darcy flows with total boundary flux, Applied Mathematics Seminar, Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, USA, Oct. 12, 2011.
  4. Longterm dynamics for well productivity index for nonlinear flows in porous media, Applied Mathematics Seminar, Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, USA, Sept. 29, 2010.
  5. Mathematical model of well productivity index for generalized Forchheimer flows and applications, Applied Mathematics Seminar, Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, USA, Sept. 16, 2009.
  6. Optimal boundary control for wave equation, Applied Mathematics Seminar, Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, USA, Oct. 1, 2008.

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