Inverse problems for nonlinear Helmholtz Schrödinger equations and time-harmonic Maxwell's equations with partial data

2022/06/30 by Lu, Xuezhu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.15006

Abstract

We consider Calderón's inverse boundary value problems for a class of nonlinear Helmholtz Schrödinger equations and Maxwell's equations in a bounded domain in \Rⁿ. 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 Calderón's inverse problem is obtained following \citeDKSU. 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.

Related

• The Calderón problem for the Schrödinger equation in transversally anisotropic geometries with partial data
• Partial data inverse problems and simultaneous recovery of boundary and\n coefficients for semilinear elliptic equations
• Partial Data Inverse Problems for the Nonlinear Schrödinger Equation
• Inverse problems for elliptic equations with power type nonlinearities
• Inverse boundary value problem for the Helmholtz equation: Multi-level approach and iterative reconstruction