The generalised Dirichlet to Neumann map for moving initial-boundary value problems
Mathematical Physics
2009-11-11 v2 math.MP
Abstract
We present an algorithm for characterising the generalised 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 ODE and on the use of the d-bar formalism. As an illustration, the Neumann boundary value for the linearised Schroedinger equation is determined in terms of the Dirichlet boundary value and of the initial condition.
Cite
@article{arxiv.math-ph/0611009,
title = {The generalised Dirichlet to Neumann map for moving initial-boundary value problems},
author = {A. S. Fokas and B. Pelloni},
journal= {arXiv preprint arXiv:math-ph/0611009},
year = {2009}
}