| Abstract: |
| In this talk, I will discuss an inverse problem for the nonlinear monodomain system. After briefly recalling the well-posedness of the direct problem for a reaction--diffusion equation coupled with an ordinary differential equation in the presence of perfectly insulating regions, I will focus on the inverse question of determining such regions from partial boundary measurements. Under suitable assumptions on the conductivity tensor, the nonlinear ionic terms, and the initial activation, I will present a uniqueness result showing that a single partial measurement of the transmembrane potential is sufficient to identify the geometry and location of the insulating inclusion. The analysis relies on a reformulation of the problem as a parabolic integro-differential equation and combines regularity estimates, a three-cylinder inequality, and unique continuation arguments. The result provides a rigorous uniqueness theorem for a class of inverse problems associated with nonlinear coupled systems of PDE--ODE type. |
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