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Overdetermined partial boundary value problems on finite networks
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes
© <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/
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.
Peer Reviewed
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
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/submittedVersion
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