Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map

TL;DR

This paper demonstrates that the linear and quadratic nonlinear components of a nonlinear elliptic equation can be uniquely identified using the Dirichlet-to-Neumann map, employing complex geometrical optics and singular solutions.

Contribution

It introduces a method to uniquely determine nonlinear terms in elliptic equations from boundary measurements, advancing inverse problem techniques.

Findings

Linear and quadratic nonlinear terms are uniquely identifiable.

The approach uses complex geometrical optics solutions.

Singular solutions are employed for proof.

Abstract

We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex geometrical optics solutions and singular solutions.