Laboratory "Numerical Aspects in Problems of Mathematical Physics"

The Laboratory was founded in 1987. It is headed by Professor A. M. Blokhin. The staff of the laboratory is: Vladimir L. Vaskevich, Ph. D., Eugenia V. Mishchenko, Ph. D., and Yuri L. Trakhinin, Ph. D.

The main field of activity of the Laboratory is study of problems of mathematical modeling in continuum mechanics, in semiconductor physics, and in electronic optics.

Promising fields of investigation at present are the following ones:

• development of a mathematical theory of strong discontinuities in various models of continuum mechanics;
• theoretical and numerical study of hydrodynamical models for charge transport in semiconductor devices;
• development of highly accurate numerical methods for finding solutions of boundary value problems for elliptic equations with application to problems of electronic optics.

The most important results obtained in the recent years were published in monographs in Russia and USA. The results on development of the mathematical theory of strong discontinuities in magnetohydrodynamics and in a superfluid liquid were presented in the monographs:

A.M.Blokhin, Strong Discontinuities in Magnetohydrodynamics. N.Y. Nova Science Publishers, Inc., 1993. 150 pp.

A.M. Blokhin, V.N. Dorovskii. Mathematical Modeling in the Theory of Multivelocity Continuum. N.Y. Nova Science Publishers, Inc., 1995. 192 pp.

The results on well-posedness of mixed problems in domains with nonsmooth boundary were presented in the monograph

A.M. Blokhin, D.L. Tkachev. Mixed Problems for the Wave Equation in Coordinate Domains. N.Y. Nova Science Publishers, Inc., 1998. 125 pp.

Different aspects of construction of numerical methods for finding solutions to hyperbolic systems were discussed in the monograph

A.M. Blokhin, R.D. Alaev. Energy Integrals and Their Applications to Investigation of Difference Schemes Stability. Novosibirsk State University, 1993, 212 pp.