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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Linear evolution equations with dynamic boundary c
onditions - Dave Smith (National University of Sin
gapore)
DTSTART;TZID=Europe/London:20191028T160000
DTEND;TZID=Europe/London:20191028T170000
UID:TALK133207AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133207
DESCRIPTION:The classical half line Robin problem for the heat
equation may be solved via a spatial Fourier tran
sform method. In this talk\, we study the problem
in which the static Robin condition $bq(0\,t)+q_x(
0\,t)=0$ is replaced with a dynamic Robin conditio
n\; $b=b(t)$ is allowed to vary in time. We presen
t a solution representation\, and justify its vali
dity\, via an extension of the Fokas transform met
hod. We show how to reduce the problem to a variab
le coefficient fractional linear ordinary differen
tial equation for the Dirichlet boundary value. We
implement the fractional Frobenius method to solv
e this equation\, and justify that the error in th
e approximate solution of the original problem con
verges appropriately. We also demonstrate an argum
ent for existence and unicity of solutions to the
original dynamic Robin problem for the heat equati
on. Finally\, we extend these results to linear ev
olution equations of arbitrary spatial order on th
e half line\, with arbitrary linear dynamic bounda
ry conditions.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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