Transport models for wave propagation in scattering media with nonlinear absorption

TL;DR

This paper develops semilinear radiative transport models for high-frequency wave propagation in highly-scattering media with nonlinear absorption, and addresses an inverse problem to reconstruct absorption coefficients with proven uniqueness.

Contribution

It introduces new semilinear transport models derived via multiscale analysis and Wigner transform, and provides a uniqueness result for the inverse absorption problem.

Findings

Derived semilinear radiative transport equations.

Established diffusive limits of the models.

Proved uniqueness in the inverse absorption problem.

Abstract

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear radiative transport models for the phase-space intensity and the diffusive limits of such transport models. As an application, we consider an inverse problem for the semilinear transport equation, where we reconstruct the absorption coefficients of the equation from a functional of its solution. We obtain a uniqueness result on the inverse problem.