Laboratory "Differential Equations of Mathematical Physics"
The Laboratory was founded in 1980.
It was headed by Academician S. K. Godunov.
The scope of scientific interests of the Laboratory staff covers a wide
variety of research fields oriented, first of all, to applications in mechanics,
physics, and engineering. At present, the head of laboratory is Prof. E.
I. Romenskii. Doctors of physical and mathematical sciences V. N. Belykh,
G. V. Demidenko, E. I. Romenskii, V. M. Gordienko
and candidates of physical and mathematical sciences S. V. Kuznetsov,
I. I. Matveeva, V. M. Cheresiz,
G. A. Chumakov work at the Laboratory.
At present, main directions of study are concentrated around the following
problems.
Modern computational linear algebra requires to develop new statements,
criteria of good conditionality and algorithms of calculation of spectral
parameters in problems with linear transformations. The results obtained
can be applied in various problems using the techniques of linear algebra
such as investigation of well-posedness in problems of mathematical physics,
stability and optimal control in differential equations. Interconnections
of well-posedness of evolutionary systems of differential equations —
conservation laws, their thermodynamic properties, and properties of invariance
under groups of transformations are investigated. The approach being developed
helps to formulate new correct models of continuous media with complex
properties.
Investigations of boundary value problems for elliptic and quasielliptic
equations and systems as well as for some classes of equations of Sobolev
type are carried on. These investigations are aimed to study the conditions
of solvability in weighted Sobolev spaces, asymptotic properties of solutions
and their regularity, singling out classes of well-posed boundary value
problems.
