Meri Lisi

Inverse Problems Related to Photon Transport in an Interstellar Cloud

Abstract In this article we study a one-dimensional mathematical model of photon transport in a homogeneous interstellar cloud, occupying a convex region, with a source of photons inside. Existence, uniqueness and positivity of the solution are proved by using the theory of semigroups. The quasi-static solution is investigated and it is shown that it is a good approximation to the exact solution. Two inverse problems are studied: the computation of the cloud dimension, and the total cross section of the cloud itself.

On the spectrum of the free streaming operator in the three‐dimensional case

We study the spectrum of the free streaming operator in the three‐dimensional case in an L 1 ‐contest. We prove that the spectrum is contained in the imaginary axis of the complex plane. We also perform a study of the semigroup generation properties of the free streaming operator and prove that the streaming operator generates a group of unitary norm in the whole space. In the half‐space case, the free streaming operator generates a group is of unitary norm only if the boundary conditions are conservative.

Algae‐Light Interaction: Study Of An Approximated Model And Asymptotic Analysis

In this paper we study the approximation of a mathematical model for the interaction of algae with light consisting of two integro‐differential equations. In particular, we integrate the system in a suitable way and we get an autonomous system of ordinary differential equations. We discuss the equilibrium solutions and study their stability. We also make an asymptotic analysis by applying the modified Chapman‐Enskog procedure.