# SIMBa: Partial boundary value problems on finite networks

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 $\Gamma=(V,c)$, we fix a proper and connected subset $F\subset V$ 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 $F$ 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 $\bar F$. 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.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a simba(at)imub(dot)ub(dot)es