Founded in 1965 as Donetsk Computing Center. Since 1970 it has been known as the Institute of Applied Mathematics and Mechanics.
Main research trends of the Institute are:
- the theory of partial differential equations and operators; constructive and geometrical theory of functions; the theory of stochastic processes and mathematical statistics;
- rigid body dynamics; the theory of stability and control; rock mechanics;
- simulation, identification and recognition of control systems.
Major research achievements:
Acad. of AS UkrSSR I. I. Daniluk made a valuable contribution to studying nonlinear free boundary problems. He constructed the generalized Morse theory, which is a major field of variation calculus “in general”, used for integral functionals with variable integration domains.
Acad. of AS UkrSSR Ya. B. Lopatinskiy developed the theory of general boundary-value problems for linear elliptic systems – an outstanding and internationally famous result.
NAS Acad. I. V. Skrypnik solved the problem on the minimal smoothness of solutions of quasi-linear elliptic high-order equations, which guarantees their regularity. He significantly refined topological methods of investigating nonlinear operator equations, applyed them to the solvability of nonlinear elliptic and parabolic boundary-value problems and developed homogenization methods for nonlinear elliptic and parabolic Dirichlet problems in perforated domains with intricate structure.
Results of Corr. Memb. of AS UkrSSR I. I. Gikhman in the theory of stochastic differential equations and stochastic processes are well-known. He introduced the notion of stochastic curvilinear integral in the random field, generalizing the notion of Ito’s integral. On this base he developed the respective stochastic analysis.
Corr. Memb. of AS UkrSSR G. D. Suvorov created new methods to investigate metric properties of mappings with bounded Dirichlet integrals, via refining the length and area principle as applied to space mappings, generalized the Caratheodory theory related to the studies of conformly invariant compact extensions of a plane domain.
NAS Corr. Memb. P. V. Kharlamov created new forms of dynamical equations describing motion of rigid body and rigid bodies systems. He produced a constructive invariant relations method and built a natural method to describe rigid body motion (godographs method).
NAS Corr. Memb. O. M. Kovaliov developed the method of oriented manifolds and the method of trajectories set. Using tthem he solved a number of important direct and inverse problems in nonlinear system control.
RAS Acad. A. M. Bogomolov, Prof., Dr. Eng., proposed and studied the algebra of structural automata and binary relations, solved the problem of general systems decomposition. He found general existence conditions for structural automata and methods to generate control and diagnostic tests, constructed the theory of probabilistic automata experiments.
