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

Journal Article · Mon Jan 15 00:00:00 EST 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2405405· OSTI ID:20929618

Fokas, A S; Pelloni, B ^[1]

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1. Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge CB3 0WA (United Kingdom)

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 spectral analysis 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 Schroedinger equation is determined in terms of the Dirichlet boundary value and of the initial conditi0008.

• OSTI ID: 20929618
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 1; Other Information: DOI: 10.1063/1.2405405; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
DIRICHLET PROBLEM
INTEGRALS
MAPS
NEUMANN SERIES
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION