Global solutions of the Landau–Lifshitz–Baryakhtar equation

Soenjaya, Agus L.; Tran, Thanh

doi:10.1016/j.jde.2023.06.033

Cited by 3 publications

(2 citation statements)

References 26 publications

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“…The model provides a detailed depiction of the three-dimensional evolution of thermodynamic and electromagnetic properties inherent in ferromagnetic materials, which can account for temperature-induced transitions from the paramagnetic to the ferromagnetic regime. The model is applicable to a wide range of temperatures [9], while the well-known Landau-Lifschitz equation can only describe magnetization dynamics at low temperatures [10][11][12][13]. The evolution of the ferromagnetic material is described by the phase transition equations referenced in [6], which are formulated as follows:…”

Section: Introductionmentioning

confidence: 99%

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Global Weak Solution for Phase Transition Equations with Polarization

Li,

2024

Mathematics

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Section: Introductionmentioning

confidence: 99%

“…If we regard polarization P as an internal field, then we can derive the electric polarization Equation ( 7), more details can be found in [20]. Substituting (11) into (10), we obtain a couple system of M, θ, E, H, and P, that is, (3)- (7).…”

Section: Introductionmentioning

confidence: 99%

Global Weak Solution for Phase Transition Equations with Polarization

Li,

2024

Mathematics

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Well-posedness and finite element approximation for the Landau–Lifshitz–Gilbert equation with spin torques

Vinod,

Tran

2024

Applicable Analysis

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Numerical method and error estimate for stochastic Landau–Lifshitz–Bloch equation

Goldys,

Jiao,

2024

IMA Journal of Numerical Analysis

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In this paper we study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau–Lifshitz–Bloch (LLB) equation on a bounded domain in ${\mathbb{R}}^{d}$ for $d=1,2$. Our main results are estimates of the rate of convergence of the Finite Element Method to the solutions of stochastic LLB. To overcome the lack of regularity of the solution in the case $d=2$, we propose a Finite Element scheme for a regularized version of the equation. We then obtain error estimates of numerical solutions and for the solution of the regularized equation as well as the rate of convergence of this solution to the solution of the stochastic LLB equation. As a consequence, the convergence in probability of the approximate solutions to the solution of the stochastic LLB equation is derived. A stronger result is obtained in the case $d=1$ due to a new regularity result for the LLB equation which allows us to avoid regularization.

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Global solutions of the Landau–Lifshitz–Baryakhtar equation

Cited by 3 publications

References 26 publications

Global Weak Solution for Phase Transition Equations with Polarization

Global Weak Solution for Phase Transition Equations with Polarization

Well-posedness and finite element approximation for the Landau–Lifshitz–Gilbert equation with spin torques

Numerical method and error estimate for stochastic Landau–Lifshitz–Bloch equation

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