- Mathematical Center in Akademgorodok
- On June 29, Timur Yskak defended his candidate's thesis "Stability of solutions of differential equations with distributed delay"
On June 29, Timur Yskak defended his candidate's thesis "Stability of solutions of differential equations with distributed delay"
June 29, 2021 at the Dissertation Council D 003.015.04 at the Sobolev Institute of Mathematics SB RAS, the defense of Timur K. Yskak's candidate's thesis "Stability of solutions of differential equations with distributed delay" took place. The thesis was carried out under the scientific supervision of doctor of physics and mathematics, professor Gennady V. Demidenko, specialty 01.01.02 — Differential equations, dynamical systems and optimal control.
The thesis is devoted to the study of differential equations with delay. Such equations arise when describing processes, the rate of which is determined not only by the present but also by the previous states. Delay equations arise in problems of automatic regulation and control, automation and telemechanics, radiophysics, in the modeling of immunological processes, in the study of gene networks, etc. In the thesis, an important problem of exponential stability of solutions of some classes of systems of differential equations with distributed delay was investigated. Sufficient conditions for the exponential stability of the zero solution of systems are obtained in terms of matrix and integral inequalities. Estimates for solutions of systems that characterize exponential decay at infinity and estimates for attraction sets for classes of nonlinear systems are established.
Timur Yskak is a member of the research project "Differential Equations and Dynamical Systems" of the Mathematical center in Akademgorodok.