Institute of Information Theory and Automation

The systems described by partial differential equations with different types of delays

Project leader: Prof. Oleksandr Rezunenko, Ph.D.
Department: AS
Supported by (ID): GA16-06678S
Grantor: Czech Science Foundation
Type of project: theoretical, applicational
Duration: 2016 - 2018
Publications at UTIA: list

Abstract:

Systems of partial differential equations (PDE) and ordinary differential equations (ODE) are studied from the point of view of Dynamical systems methods. Many problems from biology, chemistry, mechanics, control, information transmission, economics and other fields are changing in time and so they can be described by different types of Dynamical systems. It is well understood that taking into account delay effects (memory) makes the mathematical models more realistic. We are interested in developing approaches for study of local and long-time asymptotic behavior of different types of solutions to delay PDEs and ODEs. An important type of delay is the state-dependent one. This type of delay seems to be the most natural from the point of view of applications (it also includes the case of constant delay) and simultaneously the most difficult from mathematical point of view. The main goal of the project is therefore to study basic properties of such systems, including a new type of dynamical state-dependent delay and coupled differential-algebraic systems of delay equations.

Project team:
Responsible for information: general
Last modification: 04.04.2016
Institute of Information Theory and Automation