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UID:DSC-16730
DTSTART;TZID=Europe/Berlin:20200109T151500
SEQUENCE:1574173156
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20200109T161500
URL:https://www.dresden-science-calendar.de/calendar/de/detail/16730
LOCATION:TUD Willers-Bau\, Zellescher Weg 12-1401069 Dresden
SUMMARY:Appleby: Explosions and explosion control in deterministic and stoc
hastic differential equations
CLASS:PUBLIC
DESCRIPTION:Speaker: Prof. Dr. John Appleby \nInstitute of Speaker: Dublin
City University\, School of Mathematical Sciences\nTopics:\n\n Location:\n
Name: TUD Willers-Bau (WIL C 129)\n Street: Zellescher Weg 12-14\n Cit
y: 01069 Dresden\n Phone: \n Fax: \nDescription: In this talk\, we give
a survey of our recent results which characterise whether solutions of aut
onomous scalar functional differential equations can be continued for all
time\, or have a finite interval of existence. In the case that the interv
al of existence is finite\, the solution often \"explodes\"\, or tends to
infinity as the end of the interval is approached. While we do not conside
r particular applications\, we note that such behaviour can be undesirable
in real-world systems\, and therefore ask whether by applying appropriate
controls\, the blow-up\, non-continuability\, or rapid growth\, of soluti
ons can be tempered. Part of the talk is therefore devoted to determining
sharp conditions on control terms\, which can be delayed or instantaneous\
, which prevent these types of unbounded behaviour. This leads us to consi
der certain special classes of differential equations with state-dependent
delay. As a simple case study\, we examine scalar equations in which the
control can be achieved by using observations at fixed instants in time\,
and in which the delayed\, controlling\, force is piecewise constant. Time
permitting\, we will consider some results for stochastic systems also. O
ur philosophy throughout is to consider relatively simple equations\, but
to try to obtain necessary and sufficient conditions on control forces and
(state-dependent) delays which achieve the appropriate control. Parts o
f the work presented are joint with Denis Patterson (Brandeis\, Boston) an
d Xuerong Mao (Strathclyde\, Glasgow).
DTSTAMP:20200808T031938Z
CREATED:20191119T101431Z
LAST-MODIFIED:20191119T141916Z
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