| Abstract: |
| In this talk, we discuss an inverse boundary value problem arising in a semilinear elliptic model motivated by cardiac electrophysiology. The model describes the stationary behavior of the transmembrane potential under pacing and involves an anisotropic conductivity tensor together with a nonlinear ionic response.
We address the problem of recovering a piecewise constant anisotropic conductivity from boundary measurements encoded by the Neumann-to-Dirichlet map. Assuming that the nonlinear coefficient and the geometry of the inclusion are known, we present a uniqueness result showing that the conductivity is uniquely determined by the boundary data.
The analysis is based on a first-order linearization of the nonlinear map around a nontrivial background state, leading to a linear elliptic problem with a strictly positive zeroth-order term. This reduction allows us to combine boundary determination techniques for anisotropic conductivities with unique continuation arguments to achieve identifiability. |
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