1. Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations
- Author
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Eric Dumas, Franck Sueur, Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF), and Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
- Subjects
Permittivity ,35L45, 35Q60 ,compensated compactness ,Bloch equation ,Mathematics::Analysis of PDEs ,Physics::Optics ,01 natural sciences ,010305 fluids & plasmas ,Theoretical Computer Science ,Strichartz estimates ,symbols.namesake ,Mathematics (miscellaneous) ,Mathematics - Analysis of PDEs ,quasi-stationary limit ,0103 physical sciences ,FOS: Mathematics ,Initial value problem ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Limit (mathematics) ,0101 mathematics ,Mathematics ,Variable (mathematics) ,Cauchy problem ,energy estimates ,010102 general mathematics ,Mathematical analysis ,Physics::Classical Physics ,Landau-Lifschitz equation ,Maxwell's equations ,Maxwell equations ,Bloch equations ,symbols ,Maxwell-Bloch equations ,Analysis of PDEs (math.AP) - 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.
- Published
- 2010