The investigation of partial functional differential equations is a relatively new branch of mathematics. The aim of the project is to investigate such partial differential equations where the state also depends on some past occurrences.
Delay equations can be naturally written in a Banach space as an abstract equation of the following form:
Here X
is a Banach space, A is a linear or nonlinear operator in X,
or 
depending whether the delay if infinite or finite.
These equations can naturally be written as an abstract Cauchy problem
in the Banach
space
, where
.
In this way the investigation of the original differential equation can be transformed to the investigation of the functional analytic properties of the operator A.
The aim of this research project is to work out this method systematically extending previous results on the subject. Main stress is laid on the asymptotic behaviour of the solutions, extensions of the theory to neutral equations and to controllability questions.
Mathematical subject classifications (2000): 34K06, 34K20, 34K40, 47D06