El proper dilluns, 26 de novembre, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Cristina Araúz Lombardía.
Universitat: Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya

Data: dilluns 26 de novembre de 2012
Hora: 12:15, cafè i galetes; 12:30, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Partial boundary value problems on finite networks
Resum: Inverse boundary-value problems were born to answer the question of whether it is possible to determine the conductivity of a body by means of boundary measurements. These problems are exponentially ill-posed since its solutions are highly sensitive to changes in the boundary data. We are mainly interested on the discrete version of the problem, that is, the inverse boundary-value problems on finite weighted networks. The aim here is to study partial inverse boundary-value problems, which are characterized by the existance of a part of the boundary where no data is known.
Given a weighted network with conductances on the edges , we fix a proper and connected subset and will consider a certain kind of boundary value problems in which the values of the functions and of their normal derivatives are known at the same part of the boundary of and there exists another part of the boundary where no data is known. We determine when there is existance and/or uniqueness of solution on . For, it is mandatory to consider the Dirichlet-to-Neumann map of the network, its kernel and a local inverse of the matrix given by this kernel. We also observe that the kernel of the Dirichlet-to-Neumann map is a Schur Complement of the Schrödinger operator of the network.
Joint work with Ángeles Carmona and Andrés M. Encinas.

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