Title:
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Overdetermined partial boundary value problems on finite networks
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Author:
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Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes |
Abstract:
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© <2015>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Abstract:
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In this study, we define a class of non-self-adjoint boundary value problems on finite networks associated with Schrodinger operators. The novel feature of this study is that no data are prescribed on part of the boundary, whereas both the values of the function and of its normal derivative are given on another part of the boundary. We show that overdetermined partial boundary value problems are crucial for solving inverse boundary value problems on finite networks since they provide the theoretical foundations for the recovery algorithm. We analyze the uniqueness and the existence of solution for overdetermined partial boundary value problems based on the nonsingularity of partial Dirichlet-to-Neumann maps. These maps allow us to determine the value of the solution in the part of the boundary where no data was prescribed. We also execute full conductance recovery for spider networks. (C) 2014 Elsevier Inc. All rights reserved. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal -Boundary value problems -Boundary value problems -Dirichlet-to-Neumann map -Inverse problem -Recovery of conductance -UNIQUENESS -Equacions diferencials ordinàries -34B Boundary value problems |
Rights:
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Document type:
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Article - Submitted version Article |
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