Oleh Perehuda, Natalya Denysenko, Svitlana Kushnirenko
abstract:
This paper develops a comprehensive approximation framework for
functional-differential equations with delays in infinite-dimensional Banach
spaces. Particular attention is devoted to the replacement of the original
delayed system by an associated evolutionary system of delay-free differential
equations. Such an approach not only simplifies the analytical treatment of
delayed dynamics, but also provides a foundation for numerical implementations
and further qualitative analysis of infinite-dimensional control systems. The
proposed approach involves partitioning the delay interval into subintervals and
constructing the corresponding system of equations that approximates the
behavior of the original system. The main result of the study shows that, as the
mesh size of the partition tends to zero, the distance between the solutions of
the delayed equation and those of the delay-free system also tends to zero.
Mathematics Subject Classification: 35R10, 35R60, 60H15
Key words and phrases: Mild solution, generator, semigroup, approximation