Stability of the essential spectrum for 2D--transport models with Maxwell boundary conditions

TL;DR

This paper investigates the spectral properties of 2D transport models with Maxwell boundary conditions, showing that the essential spectrum remains unchanged between collisional and collisionless semigroups across various L^p spaces.

Contribution

It establishes the equivalence of the essential spectrum for collisional and collisionless semigroups in 2D transport models with Maxwell boundary conditions, linking resolvent and semigroup approaches.

Findings

Essential spectrum of full transport semigroup equals that of collisionless semigroup.

Results hold across all L^p spaces with 1<p<∞.

Applicable to three different 2D transport models.

Abstract

We discuss the spectral properties of collisional semigroups associated to various models from transport theory by exploiting the links between the so-called resolvent approach and the semigroup approach. Precisely, we show that the essential spectrum of the full transport semigroup coincides with that of the collisionless transport semigroup in any $L^p$--spaces $(1 <p < \infty)$ for three 2D--transport models with Maxwell--boundary conditions.