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arXiv · 2206.15006

Inverse problems for nonlinear Helmholtz Schr\"odinger equations and time-harmonic Maxwell's equations with partial data

Xuezhu Lu
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Abstract

We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the Dirichlet-to-Neumann map of the corresponding equations. The local uniqueness of the linearized partial data Calder\'{o}n's inverse problem is obtained following \cite{DKSU}. The Runge approximation properties and unique continuation principle allow us to extend to global situations. Simultaneous recovery of some unknown cavity$/$boundary and coefficients are given as some applications.

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Xuezhu Lu. 2022-06-30. Inverse problems for nonlinear Helmholtz Schr\"odinger equations and time-harmonic Maxwell's equations with partial data. https://arxiv.org/abs/2206.15006

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