2001   |   Professor of Mathematics.
St. Petersburg (Leningrad) State University 1977, Ph.D
CH 304A   |   907-474-5023
s.avdonin@alaska.edu

My current research is focused on the development of methods and algorithms for solving control and identification problems for distributed parameter systems. These problems have important applications in science and engineering. My approach is based on deep and heretofore incompletely exploited connections between nonharmonic Fourier series, control theory for partial differential equations, inverse problems of mathematical physics, and signal processing. This approach is now recognized by specialists, and I collaborate with many mathematicians, scientists and engineers all over the world in developing my methods, in particular, the efficient boundary control method in inverse theory.

Using this approach we have recently solved several outstanding problems in several areas of applied mathematics including:

• Control and inverse problems for partial differential equations on graphs. These equations are used to describe many physical processes such as mechanical vibrations flexible beams or strings, propagation of electro-magnetic waves in networks of optical fibers, heat flow in multi-link networks, and also electron flow in quantum mechanical circuits;
• Control and identification problems for systems with internal damping and hybrid systems. This will have important applications in many areas, such as material science, nondestructive testing, acoustic imaging, and remote sensing.

Highlighted works:

Avdonin and J. Edward, An inverse problem for quantum trees, Networks and Heterogeneous

Media, (2021), 16, No. 2, 317--339.

Avdonin, A. Mikhaylov, V. Mikhaylov, and J. Park*, Inverse Problem for the Schrodinger Equation with Non-self-adjoint Matrix Potential, Inverse Problems, (2021), 37, 035002 (19pp).
Avdonin and Y. Zhao*, Leaf peeling method for the wave equation on metric tree graphs, Inverse Problems and Imaging, (2021), 15, No. 2, 185--199.
Avdonin, Y. Zhao*, Exact controllability of the 1-d wave equation on finite metric tree graphs,

Appl. Math. Optim., (2021), 83, No. 3, 2303--2326.

S.A. Avdonin and S.A. Ivanov, Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems, Cambridge University Press, 1995, New York, London, Melbourne.

   *denotes UAF graduate students