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SUMMARY:Linear evolution equations with dynamic boundary conditions - Dave
  Smith (National University of Singapore)
DTSTART:20191028T160000Z
DTEND:20191028T170000Z
UID:TALK133207@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The classical half line Robin problem for the heat equation ma
 y be solved via a spatial Fourier transform method. In this talk\, we stud
 y the problem in which the static Robin condition $bq(0\,t)+q_x(0\,t)=0$ i
 s replaced with a dynamic Robin condition\; $b=b(t)$ is allowed to vary in
  time. We present a solution representation\, and justify its validity\, v
 ia an extension of the Fokas transform method. We show how to reduce the p
 roblem to a variable coefficient fractional linear ordinary differential e
 quation for the Dirichlet boundary value. We implement the fractional Frob
 enius method to solve this equation\, and justify that the error in the ap
 proximate solution of the original problem converges appropriately. We als
 o demonstrate an argument for existence and unicity of solutions to the or
 iginal dynamic Robin problem for the heat equation. Finally\, we extend th
 ese results to linear evolution equations of arbitrary spatial order on th
 e half line\, with arbitrary linear dynamic boundary conditions.
LOCATION:Seminar Room 1\, Newton Institute
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