Control theory of distributed parameter systems
Nonharmonic Fourier series
Inverse problems of mathematical physics
Signal processing (sampling and interpolation of band-limited and multi-band signals, spectral estimation)
Partial differential and differential-difference equations
Control and inverse problems for differential equations on graphs
Biography
ACADEMIC DEGREES
Doctor of Science in Mathematics, St. Petersburg (Leningrad) State University, 1991
Ph.D. in Mathematics, St. Petersburg (Leningrad) State University, 1977
M.S. in Physics and Mathematical Physics, St. Petersburg (Leningrad) State University, 1972
EMPLOYMENT 2012-presentProfessor, Chair of Excellence in Applied Mathematics Department of Mathematics, University of Tennessee at Chattanooga 2001-presentProfessor Department of Mathematics and Statistics University of Alaska Fairbanks 2000-2001Visiting Professor Department of Mathematics University of Tennessee, Knoxville 1991-2001Professor Department of Applied Mathematics St. Petersburg State University, Russia 1998-2001Senior Research Fellow Department of Mathematics and Statistics The Flinders University of South Australia 1995-97Professor and Head Department of Mathematics St. Petersburg University of Economics and Engineering, Russia 1983-91Associate Professor,
1980-83Assistant Professor,
1977-80Research Associate
Department of Applied Mathematics, St. Petersburg State University, Russia
SHORT TERM VISITING APPOINTMENTS January-March 2013 Visiting Research Professor, Mittag-Lefler Mathematical Institute Stockholm, Sweden June 2011 Visiting Professor, University of Valenciennes, France January 2011 Visiting Professor, University of Morelia, Mexico June 2010 Visiting Research Professor, Polytechnical University of Turin, Italy June 2009 Visiting Research Professor, University of Linköping, Sweden April 2009 Visiting Research Professor, University of Erlangen-Nurenberg, Germany March 2009 Visiting Research Professor, Polytechnical University of Turin, Italy February 2009 Visiting Professor, University of Nancy, France October-November 2008 Visiting Research Professor (Miller Scholar) University of Missouri Columbia July 2008 Visiting Research Professor, University of Erlangen-Nurenberg, Germany March-April 2007 Visiting Research Professor, Isaac Newton Mathematical Institute Cambridge, UK June 2004 Visiting Research Professor, University of Linköping, Sweden June-August, 2002; January 2003 Visiting Research Professor The Flinders University of South Australia February-March, 1999 Visiting Professor, University of Nancy, France March-April, 1997; January-February, 1996 Visiting Research Professor (grant NSF) Virginia Tech. and University of Maryland Baltimore County February-March, 1993 Visiting Research Professor (grant of the National Academy of Sciences) University of Maryland Baltimore County January 1993 (grant of the Center for Optimization and Control, Germany) University of Bayreuth, Germany September 1983-August 1984 Senior Research Fellow Lorand Eötvös University, Budapest, Hungary
AWARDS 2012 Usibelli Research Award, University of Alaska Fairbanks 2011 Visiting Distinguished Professor, Mexican Academy of Sciences 2009 Scholarship of the Italian Academy of Sciences 2008 Miller Scholarship, University of Missouri Columbia 1977 First Prize of St. Petersburg (Leningrad) State University for Young Scientists
GRANTS 2013-2016 Australian Research Council grant "Interrogation and Estimation of Differential Equation Networks" (with W. Moran and M. Morelande) 2007-2011 NSF grant "Boundary Inverse Problems in Glaciology" (with M. Truffer and D. Maxwell) 2004-2008 NSF grant "The Basal Velocity Field of a Glacier: An Inverse Approach" (with M. Truffer) 2003-2004 US National Academy of Sciences grant "Control and inverse problems for distributed parameter systems on graphs" 2003-2004 DOD grant "Spintronics", Senior Investigator 1998-2001 Grant of the Australian Research Council "Boundary control in sampling and interpolation of band-limited signals" (with W. Moran) 1997-2000 Grant of the Russian Foundation of Basic Research "Controllability problems for hybrid systems" 1995-98 NSF International Research Grant, USA, "Bases of exponentials in control of distributed parameter systems" (with D. Russell and T. Seidman) 1995-97 Grant of the Russian Foundation of Basic Research "Boundary control in inverse problems of mathematical physics" 1994-96 ESPRIT grant of the Commission of the European Communities, Senior Investigator, group leader of the subproject "Control and inverse problems for partial differential equations" 1994-95 Grant of the International Science Foundation "Nonharmonic Fourier series in control theory" 1993 Grant of the International Science Foundation "Riesz bases of vector-valued exponentials" 1992-93 Grant of the University Research Program, Russia "Inverse problem for multi-channel acoustic system"
PROFESSIONAL MEMBERSHIPS / ORGANIZATIONS / JOURNALS 2010-present Associate Editor, International Journal of Applied Math. and Computer Science 2011-present Associate Editor, Vestnik St. Petersburg University: Applied Mathematics 2013-present Associate Editor, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences = Vestnik Samara University: Mathematics Organizer, Minisymposium "Differential Equations on Graphs and their Applications", International Congress on Industrial and Applied Mathematics, Vancouver, July 2011 Organizer, Special Session "Theory and Applications of Differential Equations on Graphs", Joint Mathematics Meeting, San Diego, January 2013 1991-present Reviewer for Mathematical Reviews 2000-present Referee for Journal of Functional Analysis; Journal of Math. Analysis and Applications; SIAM Journal of Control and Optimization; Applied Mathematics and Optimization; International Journal of Applied Math. and Computer Science; Journal of Optimization and Applications; Automatica; Control, Optimization and Calculus of Variations; Asymptotic Analysis; Portugalaie Matematica; Inverse Problems; Applicable Analysis; Nonlinear Analysis
Grant proposals referee for NSF, CRDF
Member of American Mathematical Society
Main publications:
Avdonin, S.; Lenhart, S.; Protopopescu, V., “Solving the dynamical inverse problem for the Schrödinger equation by the boundary control method”, Inverse Problems, 18:2 (2002), 349–361
Avdonin, S.; Mikhaylov, V.; Rybkin, A., Communications in Mathematical Physics, 275:3 (2007), 791–803
Maxwell, D.; Truffer, M.; Avdonin, S.; Stuefer, M., “An iterative scheme for determining glacier velocities and stresses”, Journal of Glaciology, 54:188 (2008), 888–898
Avdonin, S.; Leugering, G.; Mikhaylov, V., “On an inverse problem for tree-like networks of elastic strings”, ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 90:2 (2010), 136–150
S. A. Avdonin, V. S. Mikhaylov, K. B. Nurtazina, “On inverse dynamical and spectral problems for the wave and Schrödinger equations on finite trees. The leaf peeling method”, Zap. Nauchn. Sem. POMI, 438 (2015), 7–21; J. Math. Sci. (N. Y.), 224:1 (2017), 1–10
2014
2.
S. A. Avdonin, V. S. Mikhaylov, “Spectral estimation problem in infinite dimensional spaces”, Zap. Nauchn. Sem. POMI, 422 (2014), 5–17; J. Math. Sci. (N. Y.), 206:3 (2015), 231–240
2011
3.
S. A. Avdonin, V. S. Mikhaylov, “Inverse source problem for the 1-D Schrödinger equation”, Zap. Nauchn. Sem. POMI, 393 (2011), 5–11; J. Math. Sci. (N. Y.), 185:4 (2012), 513–516
2010
4.
A. V. Arguchintsev, S. A. Avdonin, V. P. Poplevko, “Optimization of hyperbolic systems with integral constraints for smooth controls”, The Bulletin of Irkutsk State University. Series Mathematics, 3:3 (2010), 28–40
2001
5.
S. A. Avdonin, S. A. Ivanov, “Exponential Riesz bases of subspaces and divided differences”, Algebra i Analiz, 13:3 (2001), 1–17; St. Petersburg Math. J., 13:3 (2002), 339–351
2000
6.
S. A. Ivanov, S. A. Avdonin, “The Levin–Golovin theorem for Sobolev spaces”, Mat. Zametki, 68:2 (2000), 163–172; Math. Notes, 68:2 (2000), 145–153
1998
7.
S. A. Avdonin, M. I. Belishev, Yu. S. Rozhkov, “Dynamical inverse problem for nonselfadjoint Sturm–Liouville operator”, Zap. Nauchn. Sem. POMI, 250 (1998), 7–21; J. Math. Sci. (New York), 102:4 (2000), 4139–4148
1995
8.
S. A. Avdonin, O. P. Germanovich, “The basis property of the family of Floquet solutions to a periodic linear equation of neutral type in Hilbert space”, Sibirsk. Mat. Zh., 36:5 (1995), 992–997; Siberian Math. J., 36:5 (1995), 853–858
1994
9.
S. A. Avdonin, M. I. Belishev, S. A. Ivanov, “The controllability in a filled domain for a multidimensional wave equation with a singular boundary control”, Zap. Nauchn. Sem. POMI, 210 (1994), 7–21; J. Math. Sci., 83:2 (1997), 165–174
1992
10.
S. A. Avdonin, O. Ya. Gorshkova, “Controllability and quasicontrollability of parabolic systems with delay”, Differ. Uravn., 28:3 (1992), 442–451; Differ. Equ., 28:3 (1992), 374–383
1991
11.
S. A. Avdonin, S. A. Ivanov, A. Z. Ishmukhametov, “A quadratic problem of the optimal control of the vibrations of a
string”, Dokl. Akad. Nauk SSSR, 316:4 (1991), 781–785; Dokl. Math., 43:1 (1991), 154–158
12.
S. A. Avdonin, M. I. Belishev, S. A. Ivanov, “Boundary control and a matrix inverse problem for the equation $u_{tt}-u_{xx}+V(x)u=0$”, Mat. Sb., 182:3 (1991), 307–331; Math. USSR-Sb., 72:2 (1992), 287–310
13.
S. A. Avdonin, O. A. Gorshkova, “Об относительной и полной квазиуправляемости параболических систем с запаздыванием”, Vestnik Chelyabinsk. Gos. Univ., 1991, 1, 141–142
1989
14.
S. A. Avdonin, S. A. Ivanov, “A generating matrix function in problems of the control of the
vibrations of connected strings”, Dokl. Akad. Nauk SSSR, 307:5 (1989), 1033–1037; Dokl. Math., 40:1 (1990), 179–183
1984
15.
S. A. Avdonin, S. A. Ivanov, “Serial bases of exponentials and the problem of damping of a
system of strings”, Dokl. Akad. Nauk SSSR, 275:2 (1984), 355–358
1977
16.
S. A. Avdonin, “Solution of the exponential moment problem in the space $L^2(0,\infty)$”, Zap. Nauchn. Sem. LOMI, 73 (1977), 193–194; J. Soviet Math., 34:6 (1986), 2137–2138
1974
17.
S. A. Avdonin, “On Riesz bases of exponential functions in $L^2$”, Zap. Nauchn. Sem. LOMI, 39 (1974), 176–177
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