Displaying similar documents to “Moving heat source reconstruction from the Cauchy boundary data.”

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.

The Calderón problem with partial data

Johannes Sjöstrand (2004)

Journées Équations aux dérivées partielles

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We describe a joint work with C.E. Kenig and G. Uhlmann [] where we improve an earlier result by Bukhgeim and Uhlmann [], by showing that in dimension n ≥ 3 , the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [] but use a richer set of solutions to the Dirichlet problem.

Diffusion and propagation problems in some ramified domains with a fractal boundary

Yves Achdou, Christophe Sabot, Nicoletta Tchou (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of ℝ 2 with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for...