Generalized Dirichlet to Neumann map for moving initial-boundary value problems
Generalized Dirichlet to Neumann map for moving initial-boundary value problems
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DOI：
10.1063/1.2405405
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发表时间：
2006-11
影响因子：
1.3
通讯作者：
A. Fokas;B. Pelloni
中科院分区：
文献类型：
--
作者：
A. Fokas;B. Pelloni
提出了一种描述移动初边值问题广义Dirichlet - Neumann映射的算法。该算法是将问题的初始值和边值耦合的所谓全局关系与对某些一维积分求反的新方法相结合而得到的。这种新方法是基于一个相关常微分方程的谱分析和d-bar形式的使用。作为一个例子，线性化薛定谔方程的诺伊曼边值是根据狄利克雷边值和初始条件确定的。
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 Schrodinger equation is determined in terms of the Dirichlet boundary value and of the initial condition.