Research Interests
Partial differential equations, control of distributed parameter systems, hydrodynamics
Education
- Ph D: Mathematical Physics, (1982), Steklov Mathematical Institute - St. Petersburg, Russia
- MS: Mathematical Physics, (1972), St.Petersburg University - St.Petersburg, Russia
Selected Awards and Honors
- Mathematics Professor of the Year, Teaching - Kappa Mu Epsilon Mathematics Honor Society, Texas Tech University
- President's Excellence in Teaching Award, Teaching - Texas Tech University
- Special recognition for Excellence in Teaching and Service, Teaching - Student Chapter of the Mathematical Association of America, Texas Tech University
- Teaching Excellence Award (2006), Teaching - University of Massachusetts Lowell
- Mathematics Professor of the Year (2003), Teaching - Kappa Mu Epsilon Mathematics Honor Society
- President's Excellence in Teaching Award (1998), Teaching - Texas Tech University
- Mathematics Professor of the Year (1997), Teaching - Kappa Mu Epsilon Mathematics Honor Society, Texas Tech University
- Special recognition for Excellence in Teaching and Service (1996), Teaching - Student Chapter of the Mathematical Association of America
- Mathematics Professor of the Year (1994), Teaching - Kappa Mu Epsilon Mathematics Honor society
- Mathematics Professor of the Year (1992), Teaching - Kappa Mu Epsilon Mathematics Honor Society
Selected Publications
- Shubov, M.A., Shubov, V. (2016). Asymptotic and spectral analysis and control problems for mathematical model of piezoelectric energy harvester. Mathematics in Engineering, Science & Aerospace (MESA), 7(2).
- Shubov, M., Shubov, V. (2016). Stability of a flexible structure with destabilizing boundary conditions. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences!!!, 472(2191) 1 - 22.
- Byrnes, C.I., Gilliam, D.S., Hu, C., Shubov, V. (2013). Asymptotic regulation for distributed parameter systems via zero dynamics inverse design. International Journal of Robust and Nonlinear Control, 23(3) 305-333.
- Byrnes, C.I., Gilliam, D.S., Hu, C., Shubov, V. (2010). Zero dynamics boundary control for regulation of the Kuramoto-Sivashinsky equation. Mathematical and Computer Modelling, 52(5-6) 875-891.
- Byrnes, C.I., Gilliam, D.S., Isidori, A., Shubov, V. (2006). Zero dynamics modeling and boundary feedback design for parabolic systems. Mathematical and Computer Modelling, 44(9-10) 857-869.
- Byrnes, C.I., Gilliam, D.S., Shubov, V., Weiss, G. (2002). Regular linear systems governed by a boundary controlled heat equation. Journal of Dynamical and Control Systems, 8(3) 341-370.
- Allen, E., Burns, J., Gilliam, D., Hill, J., Shubov, V. (2002). The impact of finite precision arithmetic and sensitivity on the numerical solution of partial differential equations. Mathematical and Computer Modelling, 35(11-12) 1165-1195.
- Byrnes, C., Hu, X., Martin, C.F., Shubov, V. (2001). Input-output behavior for stable linear systems. Journal of the Franklin Institute, 338(4) 497-507.
- Balogh, A., Gilliam, D.S., Shubov, V. (2001). Stationary solutions for a boundary controlled burgers' equation. Mathematical and Computer Modelling, 33(1-3) 21-37.
- Byrnes, C.I., Lauk�, I.G., Gilliam, D.S., Shubov, V. (2000). Output regulation for linear distributed parameter systems. IEEE Transactions on Automatic Control, 45(12) 2236-2252.
- Byrnes, C.I., Gilliam, D.S., Shubov, V. (1999). Boundary control, stabilization and zero-pole dynamics for a non-linear distributed parameter system. International Journal of Robust and Nonlinear Control, 9(11) 737-768.
- Byrnes, C.I., Lauko, I.G., Gilliam, D.S., Shubov, V. (1998). Conditions for solvability of the output regulator problem for SISO distributed parameter systems. Proceedings of the IEEE Conference on Decision and Control, 3 2392-2393.
- Byrnes, C.I., Gilliam, D.S., Lauko, I.G., Shubov, V. (1998). Harmonic forcing for linear distributed parameter systems. Journal of Mathematical Systems, Estimation, and Control, 8(2) 201-204.
- Burns, J., Balogh, A., Gilliam, D.S., Shubov, V. (1998). Numerical stationary solutions for a viscous Burgers' equation. Journal of Mathematical Systems, Estimation, and Control, 8(2) 253-256.
- Byrnes, C.I., Gilliam, D.S., Shubov, V. (1998). On the global dynamics of a controlled viscous burgers' equation. Journal of Dynamical and Control Systems, 4(4) 457-519.
- Byrnes, C.I., Lauko, I.G., Gilliam, D.S., Shubov, V. (1998). Zero dynamics for relative degree one SISO distributed parameter systems. Proceedings of the IEEE Conference on Decision and Control, 3 2390-2391.
- Byrnes, C.I., Gilliam, D.S., Shubov, V. (1996). High gain limits of trajectories and attractors for a boundary controlled viscous Burgers' equation. Journal of Mathematical Systems, Estimation, and Control, 6(4) 485-488.
- Martin, C., Shubov, V. (1993). Natural exponential families of probability distributions and exponential-polynomial approximation. Applied Mathematics and Computation, 59(2-3) 275-297.
- Martin, C., Shubov, V. (1993). Probability measures, appel polynomials and polynomial approximation. Applied Mathematics and Computation, 53(2-3) 277-298.
- Shubov, V. (1990). Subsets of a Hilbert space, having finite hausdorff dimension. Journal of Soviet Mathematics, 49(5) 1217-1224.
- Shubov, V. (1988). Existence of a weak solution of Bogolyubov's hierarchical equations for infinite classical anharmonic systems with constraints. Journal of Soviet Mathematics, 40(5) 690-700.
- Shubov, V. (1987). Dynamics of infinite classical anharmonic systems with constraints. Journal of Soviet Mathematics, 37(1) 909-913.
- Shubov, V. (1985). Unique solvability of the Cauchy problem for the equations of discrete chiral fields with values in Riemannian manifolds. Journal of Soviet Mathematics, 30(4) 2353-2368.
- Shubov, V. (1984). Unique solvability of the cauchy problem for the equations of discrete multidimensional chiral fields, taking values on the unit sphere. Journal of Soviet Mathematics, 24(5) 633-638.
- Ladyzhenskaya, O.A., Shubov, V. (1984). Unique solvability of the Cauchy problem for the equations of the two-dimensional relativistic chiral fields, taking values in complete Riemann manifolds. Journal of Soviet Mathematics, 25(1) 855-864.
- Shubov, V. (1982). Classification of the reductions of the equations of principal chiral fields. Functional Analysis and Its Applications, 16(3) 239-240.
- Shubov, V. (1979). Finding of N-soliton solutions of multidimensional nonlinear equations by means of Hirota's method. Theoretical and Mathematical Physics, 41(1) 891-895.
- Shubov, V. (1977). The decomposition of a quasiregular representation of the Lie group by the orbit method. Journal of Soviet Mathematics, 8(2) 229-246.
Selected Presentations
- Mathematical Analysis of Fluid Flow Through a Compliant Tube, January 2010 - Flight Systems Research Center at UCLA
- Instability of Viscous Flow in Channel with Flexible Walls - 7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, May 2008 - Arlington, Texas
- Linear Stability Analysis of Blood Flow Model - SIAM Conference on Analysis of Partial Differential Equations, July 2006 - Boston, Massachusetts, United States
- Existence, Regularity, and Limit Behavior for Coupled System of Navier-Stokes and Euler Equations - International Workshop on Fluid-Structure Interaction, September 2005 - UCLA
- Small scale spatial mollifiers and output regulation with infinite dimensional ecosystems, 2003 - Mittag - Leffler Mathematical Institute, Swedish Royal Academy of Science, Stockholm, Sweden
- , August 2003 - UCLA
- Dynamics of fluid suspensions and dusty airflows, February 2003 - Florida State University, Tallahassee, FL
- Regular Linear Systems Governed by Parabolic Equations - Texas PDE Conference, February 2002 - San Antonio, TX
- Dynamics of airflows containing dust particles and of fluid suspensions. Applications to tornado dynamics - Minisymposium on Dynamics and Control of Fluid Flows, 5th International Control Conference, July 2001 - San Diego
- Fine dust limit for coupled systems of Navier-Stokes and Euler equations - 3rd International Conference on Nonlinear Problems in Aviation and Aerospace, May 2000 - Daytona Beach, FL
- Stability of airflow containing dust and applications to tornado dynamics - International Conference on Differential Equations and Dynamical Systems, May 2000 - Kennesaw State University, Atlanta, GA
- Equations of dusty flows and stability of tornado vortex, August 1999 - Center for Wind Engineering Research Civil Engineering at Texas Tech
- Control of vortex flows and tornado models - special session on "Control of Fluids Flows" at the SIAM Annual Meeting, May 1999 - Atlanta, GA
- High gain limit of trajectories and semiglobal stabilization of boundary controlled viscous Burgers' equation, November 1998 - Department of Applied Mechanics and Engineering Science the University of California at San Diego
- Feedback regularization of Navier-Stokes equations - 5th International Symposium on Methods and Models in Automation and Robotics, August 1998 - Miedzyzdroje, Poland
- Feedback control of Navier-Stokes system - SIAM Conference on Systems and Control, May 1998 - Jacksonville, Florida
- Output Regulation for Distributed Parameter Systems Governed by Parabolic Equations - Conference on Analysis of Partial Differential Equations, December 1997 - Phoenix, Arizona
Selected Contracts, Fellowships, Grants and Sponsored Research
- Supplemental ARP Grant for Ropes High math teacher Danny McNabb (), Grant - ARP
- PI: Mathematical Analysis of Tornado Dynamics (1997), Sponsored Research - Texas Advanced Research Program
- Consultant: Nonlinear Control Systems (2003), Grant - Washington University, St. Louis
- Consultant: Nonlinear Control Systems (2000), Grant - Washington University, St. Louis
- Consultant: Nonlinear Control Systems (1997), Grant - Washington University, St. Louis
- Supplemental ARP Grant for Coronado High School math teacher Joe Hill (1999), Grant - ARP
- Nonlinear Control Systems (Consultant) (1994), Grant - Air Force Office of Scientific