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Dirichlet-to-Neumann Mapping for the Characteristic Elliptic Equations with Symmetric Periodic Coefficients

Published online by Cambridge University Press:  03 June 2015

Jingsu Kang ,
Meirong Zhang  and
Chunxiong Zheng
Jingsu Kang*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China
Meirong Zhang*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China
Chunxiong Zheng*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China
*
Email:691675583@qq.com
Email:mzhang@math.tsinghua.edu.cn
Corresponding author.Email:czheng@math.tsinghua.edu.cn
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Abstract

Based on the numerical evidences, an analytical expression of the Dirichlet-to-Neumann mapping in the form of infinite product was first conjectured for the one-dimensional characteristic Schrödinger equation with a sinusoidal potential in [Commun. Comput. Phys., 3(3): 641-658, 2008]. It was later extended for the general second-order characteristic elliptic equations with symmetric periodic coefficients in [J. Comp. Phys., 227: 6877-6894, 2008]. In this paper, we present a proof for this Dirichlet-to-Neumann mapping.

Keywords

65M9981-08Dirichlet-to-Neumann mappingSchrödinger equationsymmetric periodic potentialsabsorbing boundary conditions
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 4 , October 2014 , pp. 1102 - 1115
Copyright
Copyright © Global Science Press Limited 2014

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