Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations
نویسندگان
چکیده
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.
منابع مشابه
Quasi-stationary Limit and a Landau-lifshitz Equation in Ferromagnetism
In this paper we study a Landau-Lifshitz equation in ferromagnetism without exchange energy as a quasi-stationary limit of a coupled Maxwell system as dielectric permittivity approaches zero. We present a different formulation and proof of this quasi-stationary limit result. We also prove a new uniqueness and stability result for the limit Landau-Lifshitz equation.
متن کاملTime Average in
In this paper we study a model of ferromagnetic material governed by a nonlinear Laudau-Lifschitz equation coupled with Maxwell equations. We prove the existence of weak solutions. Then we prove that all points of the !-limit set of any trajectories are solutions of the stationary model. Furthermore we derive rigourously the quasistatic model by an appropriate time average method.
متن کاملA pr 1 99 8 On a Singular Limit Problem for Nonlinear Maxwell ’ s Equations
In this paper we study the following nonlinear Maxwell’s equations εEt+σ(x, |E|)E = ∇×H+F, Ht+∇×E = 0, where σ(x, s) is a monotone graph of s. It is shown that the system has a unique weak solution. Moreover, the limit of the solution as ε → 0 converges to the solution of quasi-stationary Maxwell’s equations. AMS(MOS) Subject Classifications: 35K20, 35Q20.
متن کاملOn Transitions to Stationary States in a Maxwell-Landau-Lifschitz-Gilbert System
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...
متن کاملSoret Dufour Driven Thermosolutal Instability of Darcy-maxwell Fluid
Linear stability of double diffusive convection of Darcy-Maxwell fluid with Soret and Dufour effects is investigated. The effects of the Soret and Dufour numbers, Lewis number, relaxation time and solutal Darcy Rayleigh number on the stationary and oscillatory convection are presented graphically. The Dufour number enhances the stability of Darcy-Maxwell fluid for stationary convection while it...
متن کامل