Inverse problems for nonlinear Helmholtz Schr\"odinger equations and time-harmonic Maxwell's equations with partial data
Analysis of PDEs
2022-07-01 v1
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 . 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 cavityboundary and coefficients are given as some applications.
Cite
@article{arxiv.2206.15006,
title = {Inverse problems for nonlinear Helmholtz Schr\"odinger equations and time-harmonic Maxwell's equations with partial data},
author = {Xuezhu Lu},
journal= {arXiv preprint arXiv:2206.15006},
year = {2022}
}