Applied Analysis Seminar - Abstracts
Talk
Thursday, 14 November 2019, 13:30-14:30 in HG02.052
Sjoerd Verduyn Lunel (Utrecht University)
Delay equations and twin semigroups
Abstract
A delay equation is a rule for extending a function of time towards the future on the basis of
the (assumed to be) known past. By translation along the extended function (i.e., by updating
the history), one defines a dynamical system. If one chooses as state-space the continuous
initial functions, the translation semigroup is continuous, but the initial data corresponding
to the fundamental solution is not contained in the state space.
In ongoing joint work with Odo Diekmann, we choose as state space the space of bounded Borel
functions and thus sacrifice strong continuity in order to gain a simple description of the
variation-of-constants formula.
The aim of the lecture is to introduce the perturbation theory framework of twin semigroups
on a norming dual pair of spaces, to show how renewal equations fit in this framework and to
sketch how neutral equations can be covered. The growth of an age-structured population serves
as a pedagogical example.
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