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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Initial-boundary value problems for the nonlinear
Schrödinger equation in one and two dimensions -
Dionyssis Mantzavinos (University of Kansas)
DTSTART;TZID=Europe/London:20220909T153000
DTEND;TZID=Europe/London:20220909T163000
UID:TALK177875AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/177875
DESCRIPTION:A method for establishing the Hadamard well-posedn
ess (existence\, uniqueness\, and continuous depen
dence of solution on the data) of dispersive parti
al differential equations in the setting of initia
l-boundary value problems has been developed in re
cent years by Athanassios Fokas\, Alex Himonas and
the speaker. In this talk\, new developments via
this method are discussed in the context of the no
nlinear Schrödinger equation and\, more specifica
lly\, for boundary conditions of Robin type in one
as well as in two spatial dimensions. The Neumann
problem is also covered as a special case. A key
role in the analysis is played by the solution for
mulae for the linear Schrödinger equation obtaine
d via Fokas's unified transform\, which are used f
or establishing suitable linear estimates that are
then combined with a contraction mapping argument
to yield well-posedness for the nonlinear problem
s. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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