Systems described by partial differential equations with delays

Differential equations form a tool that is frequently used for describing a great variety of dynamical systems.
The developed theory of differential equations gives a possibility to study different kinds of processes like those with a finite number of degrees of freedom (ordinary differential equations), systems with distributed
parameters (partial differential equations), systems with memory (differential equations with delays),... A lot of attention has recently been paid to a new class of differential equations with delays where the delays
can change according to particular states of the system. Using this kind of equations, many systems - found for example in technology, physics, biology and chemistry - that cannot be dealt with other types of differential equations can be described. The main goal of the project is therefore to study basic properties of such systems, namely to describe qualitative properties of solutions and find sufficient conditions for well-posedness.