A Guide to the Russian Academy of Sciences - University of Texas ...

identification of aerodynamic parameters, environmental monitoring.
Development of algorithms and programs for control of the gazlift
process of oil recovery.
Section of Non-linear Analyses
The main subjects of the investigations realized in the Section of Non-linear Analyses are:
the non-linear differential equations
non-regular problems of dynamic optimization
their extensions to generalized functions.
These investigations have resulted in the following.
The general scheme of divergence removing has been developed. The correctness condition
of Hadamard in the spaces of generalized functions has been found (V. K. Ivanov).
The theory of non-linear operators in terms of convolutions has been constructed in the
spaces of functionals (V. K. Ivanov, V. V. Perminov).
The theory of non-stationary linear operators in the space of the distributions has been
developed (S. T. Zavalishchin).
The special product of generalized functions has been constructed. On the basis of this
construction the correct extension of certain classes of non-linear differential
equations to the spaces of generalized functions has been realized. These results
have been applied to the problems of extension of mathematical models of
manipulator motion in the viscous medium, the variable mass point motion in the
central gravitational field with impulse control and to the problem of the extension
of the Shrediger equation for stationary particle to the situation of pointwise
potentials as well. These new models permit to solve some practical problems of
dynamic optimization, resulted in impulse optimal control (S. T. Zavalishchin, V.
V. Revenko).
The integral inclusion as the extension of non-linear differential equation to the distributions
has been obtained. The problem of continuous dependence of the approximated
solutions on the right parts of the equation has been investigated. The impulse
extension in the energetic functional optimization problem has been constructed (A.
N. Sesekin).
The basis of the theory of the singular linear differential equations in the spaces of
generalized functions has been developed (F. Z. Rafikov).
System Software Department
Personnel:
Averbukh Vladimir Lazarevich
Ermakov Dmitri Germanovich
Igumnov Aleksandr Stanislavovich
Petrov Alexei Nickolaevich
Samofalov Victor Vladimirovich
Solovieva Li'a Alexandrovna
Sundukova Klavdiya Andreevna
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