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The purpose of this note is to present some mathematical results on thin ferromagnetic films with... more The purpose of this note is to present some mathematical results on thin ferromagnetic films with surface anisotropy energy. The model considered is described by the Landau-Lifshitz-Gilbert equations supplemented with Rado-Weertman boundary conditions expressing the surface anisotropy energy, coupled to Maxwell’s equations. We prove global existence results and discuss the behaviour of the solutions when the thickness of the film tends to 0.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Annales de l Institut Henri Poincare (C) Non Linear Analysis
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Bollettino dell Unione Matematica Italiana
Proceedings of the Royal Society of Edinburgh Section A Mathematics
Asymptotic Analysis
The effect of thin ferromagnetic films is studied in this paper. We shall adopt the Landau-Lifsch... more The effect of thin ferromagnetic films is studied in this paper. We shall adopt the Landau-Lifschitz-Gilbert equation as a phenomenological model for the ferromagnetic materials. Asymptotic analysis of the fields and the magnetization vector inside thin ferromagnetic films are performed and their convergences are established. Our results reveal the physical nature of this nonlinear model. They also provide an effective method for overcoming the computational difficulties that arise in thin ferromagnetic coatings.
Asymptotic Analysis
We consider, in the nonsteady-state case, the problem of emitted charged particles in a plane dio... more We consider, in the nonsteady-state case, the problem of emitted charged particles in a plane diode. This problem is described by the Vlasov–Poisson system with singular data converging to some Dirac measures in the velocity space concentrated at t = 0. Under a sufficient condition on the data, which implies that the particles emitted from the cathode are all collected by the anode, we prove that the solutions converge to a measure solution, with support on velocity, of the Vlasov–Poisson system.
This paper is concerned with global existence of weak solutions to a model equations of magnetiza... more This paper is concerned with global existence of weak solutions to a model equations of magnetization reversal by spin-polarized current in a layer introduced in [18]. The local magnetization of the ferromagnet satisfies the usual Landau-Lifshitz equation which is coupled to the nonlinear heat equation satisfied by the spin accumulation field defined in all the layer. The coupling is due to the contact interaction energy. We use an hyperbolic regularization method with penalization of the saturation constraint satisfied by the local magnetization to prove global existence result, in any finite time interval, of weak solutions with finite energy. We present other models of equations describing the magnetization switching by spin-polarized current and show that our method can be used to solve them.
Journal of Mathematical Fluid Mechanics, 2014
ABSTRACT We discuss the equations describing the dynamic of the heat transfer in a magnetic fluid... more ABSTRACT We discuss the equations describing the dynamic of the heat transfer in a magnetic fluid flow under the action of an applied magnetic field. Instead of the usual heat transfer equation we use a generalization given by the Maxwell–Cattaneo law which is a system satisfied by the temperature and the heat flux. We prove a global existence of weak solutions to the system having a finite energy.
The present paper is particularly devoted to the damping eect in ferromagnetic materials. We are ... more The present paper is particularly devoted to the damping eect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method so- lution to the phenomenological damping parameter . We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter tends either to 0 (underdamped case) or +1 (overdamped case).
The purpose of this note is to present some mathematical results on thin ferromagnetic films with... more The purpose of this note is to present some mathematical results on thin ferromagnetic films with surface anisotropy energy. The model considered is described by the Landau-Lifshitz-Gilbert equations supplemented with Rado-Weertman boundary conditions expressing the surface anisotropy energy, coupled to Maxwell’s equations. We prove global existence results and discuss the behaviour of the solutions when the thickness of the film tends to 0.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Annales de l Institut Henri Poincare (C) Non Linear Analysis
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Bollettino dell Unione Matematica Italiana
Proceedings of the Royal Society of Edinburgh Section A Mathematics
Asymptotic Analysis
The effect of thin ferromagnetic films is studied in this paper. We shall adopt the Landau-Lifsch... more The effect of thin ferromagnetic films is studied in this paper. We shall adopt the Landau-Lifschitz-Gilbert equation as a phenomenological model for the ferromagnetic materials. Asymptotic analysis of the fields and the magnetization vector inside thin ferromagnetic films are performed and their convergences are established. Our results reveal the physical nature of this nonlinear model. They also provide an effective method for overcoming the computational difficulties that arise in thin ferromagnetic coatings.
Asymptotic Analysis
We consider, in the nonsteady-state case, the problem of emitted charged particles in a plane dio... more We consider, in the nonsteady-state case, the problem of emitted charged particles in a plane diode. This problem is described by the Vlasov–Poisson system with singular data converging to some Dirac measures in the velocity space concentrated at t = 0. Under a sufficient condition on the data, which implies that the particles emitted from the cathode are all collected by the anode, we prove that the solutions converge to a measure solution, with support on velocity, of the Vlasov–Poisson system.
This paper is concerned with global existence of weak solutions to a model equations of magnetiza... more This paper is concerned with global existence of weak solutions to a model equations of magnetization reversal by spin-polarized current in a layer introduced in [18]. The local magnetization of the ferromagnet satisfies the usual Landau-Lifshitz equation which is coupled to the nonlinear heat equation satisfied by the spin accumulation field defined in all the layer. The coupling is due to the contact interaction energy. We use an hyperbolic regularization method with penalization of the saturation constraint satisfied by the local magnetization to prove global existence result, in any finite time interval, of weak solutions with finite energy. We present other models of equations describing the magnetization switching by spin-polarized current and show that our method can be used to solve them.
Journal of Mathematical Fluid Mechanics, 2014
ABSTRACT We discuss the equations describing the dynamic of the heat transfer in a magnetic fluid... more ABSTRACT We discuss the equations describing the dynamic of the heat transfer in a magnetic fluid flow under the action of an applied magnetic field. Instead of the usual heat transfer equation we use a generalization given by the Maxwell–Cattaneo law which is a system satisfied by the temperature and the heat flux. We prove a global existence of weak solutions to the system having a finite energy.
The present paper is particularly devoted to the damping eect in ferromagnetic materials. We are ... more The present paper is particularly devoted to the damping eect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method so- lution to the phenomenological damping parameter . We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter tends either to 0 (underdamped case) or +1 (overdamped case).