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SUMMARY:Initial-boundary value problems for the nonlinear Schrödinger eq
 uation in one and two dimensions - Dionyssis Mantzavinos (University of Ka
 nsas)
DTSTART:20220909T143000Z
DTEND:20220909T153000Z
UID:TALK177875@talks.cam.ac.uk
DESCRIPTION:A method for establishing the Hadamard well-posedness (existen
 ce\, uniqueness\, and continuous dependence of solution on the data) of di
 spersive partial differential equations in the setting of initial-boundary
  value problems has been developed in recent years by Athanassios Fokas\, 
 Alex Himonas and the speaker. In this talk\, new developments via this met
 hod are discussed in the context of the nonlinear Schrödinger equation a
 nd\, more specifically\, for boundary conditions of Robin type in one as w
 ell 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 formul
 ae for the linear Schrödinger equation obtained via Fokas's unified tran
 sform\, which are used for establishing suitable linear estimates that are
  then combined with a contraction mapping argument to yield well-posedness
  for the nonlinear problems.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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