| Abstract: |
| The main purpose of this talk is to present recent results on the Calder\`{o}n problem for nonlocal wave equations with polyhomogeneous nonlinearities. We start by discussing the unique determination of homogeneous nonlinearities from the Dirichlet to Neumann map. Then, we explain how this approach can be generalized to recover polyhomogeneous nonlinearities. On the way, we discuss an optimal Runge approximation result, which in turn relies on the existence of very weak solutions to linear nonlocal wave equations with sources in $L^2(0,T;H^{-s}(\Omega))$. |
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