Identification of the coefficients in the linear Boltzmann equation by a finite number of boundary measurements

TL;DR

This paper proves that the coefficients in the time-dependent linear Boltzmann equation can be uniquely identified using a finite number of boundary measurements, assuming the coefficients are in a finite-dimensional space.

Contribution

It establishes a finite measurement uniqueness result for the inverse problem of identifying coefficients in the linear Boltzmann equation.

Findings

Total extinction coefficient and collision kernel are uniquely determined by at most k boundary measurements.

Unique identification holds when coefficients are in a finite k-dimensional vector space.

The result applies to the time-dependent linear Boltzmann equation.

Abstract

In this paper we consider an inverse problem for the time dependent linear Boltzmann equation. It concerns the identification of the coefficients via a finite number of measurements on the boundary. We prove that the total extinction coefficient and the collision kernel can be uniquely determined by at most k measurements on the boundary, provided that these coefficients belong to a finite k-dimensional vector space.