Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation

TL;DR

This paper introduces a method for simultaneously recovering multiple coefficients in a semilinear elliptic equation using higher order linearization and monotonicity, based on partial boundary data.

Contribution

It develops a novel approach combining higher order linearization and monotonicity to recover diffusion, cavity, and coefficients simultaneously from partial data.

Findings

Successful simultaneous recovery of coefficients and cavity.

Applicable to partial boundary data scenarios.

Advances inverse problem techniques for semilinear elliptic equations.

Abstract

In this short note, we investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data. The main technique is based on higher order linearization and monotonicity approaches. With these methods at hand, we can determine the diffusion, cavity and coefficients simultaneously by knowing the corresponding localized Dirichlet-Neumann operators.