Generalized Dirichlet to Neumann map for moving initial-boundary value problems

A. S. Fokas, Beatrice Pelloni

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19 Citations (Scopus)

Abstract

We present an algorithm for characterizing the generalized Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectralanalysis of an associated ordinary differantial equation and on the use of the d-bar formalism. As an illustration, the Neumann boundary value for the linearized Schrödinger equation is determined in terms of the Dirichlet boundary value and of the initial condition.
Original languageEnglish
Article number013502
JournalJournal of Mathematical Physics
Volume48
Issue number1
DOIs
Publication statusPublished - Jan 2007

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