Displaying similar documents to “Inverse boundary value problems for partial differential equations.”

30 Years of Calderón’s Problem

Gunther Uhlmann (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.

Determining of right-hand side of higher order ultraparabolic equation

Nataliya Protsakh (2017)

Open Mathematics

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In the paper the conditions of the existence and uniqueness of the solution for the inverse problem for higher order ultraparabolic equation are obtained. The equation contains two unknown functions of spatial and time variables in its right-hand side. The overdetermination conditions of the integral type are used.

Anisotropic inverse problems and Carleman estimates

David Dos Santos Ferreira (2007-2008)

Séminaire Équations aux dérivées partielles

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This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann []. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding...

The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion

Isaac Harris (2022)

Applications of Mathematics

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In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spatial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem...