**Viktor Shubov**Professor

- CollegeCollege of Sciences
- DepartmentMathematical Science
- Phone978-934-2420
- OfficeSouthwick 304C
- Email

## Expertise

Partial differential equations, control of distributed parameter systems, hydrodynamics

## 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*