Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations

TL;DR

This paper extends the analysis of the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations to variable magnetic permeability and electric permittivity, focusing on the Cauchy problem and quasi-stationary limit.

Contribution

It introduces new results for the Cauchy problem and quasi-stationary limit with variable material properties in these equations.

Findings

Extended previous results to variable permeability and permittivity

Established well-posedness of the Cauchy problem under new conditions

Analyzed the quasi-stationary limit in the variable coefficient setting

Abstract

In this paper we continue the investigation of the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations. In particular we extend some previous results about the Cauchy problem and the quasi-stationary limit to the case where the magnetic permeability and the electric permittivity are variable.