Existence of Regular Solutions of the Landau--Lifshitz--Gilbert Equation in 3D with Natural Boundary Conditions

DOI10.1137/16M1103427zbMath1382.35245OpenAlexW2768282495MaRDI QIDQ4594915

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Publication date: 27 November 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1103427

zbMATH Keywords

well-posednesssolvabilityregular solutionsLandau-Lifshitz-Gilbert equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) Stability and convergence of numerical methods for ordinary differential equations (65L20) PDEs in connection with quantum mechanics (35Q40) Statistical mechanics of ferroelectrics (82D45) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (11)

A framework of the finite element solution of the Landau-Lifshitz-Gilbert equation on tetrahedral meshes ⋮ Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics ⋮ On the Multiscale Landau–Lifshitz–Gilbert Equation: Two-Scale Convergence and Stability Analysis ⋮ FEM-BEM coupling for the Maxwell-Landau-Lifshitz-Gilbert equations via convolution quadrature: weak form and numerical approximation ⋮ Global solutions of the Landau-Lifshitz-Baryakhtar equation ⋮ The Landau-Lifshitz-Bloch equation in the thin film ⋮ Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics ⋮ Unconditional optimal error estimates of linearized second-order BDF Galerkin FEMs for the Landau-Lifshitz equation ⋮ The estimates of the ill-posedness index of the (deformed-) continuous Heisenberg spin equation ⋮ Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation ⋮ Spin-diffusion model for micromagnetics in the limit of long times

Cites Work

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• A convergent finite element approximation for the quasi-static Maxwell-Landau-Lifshitz-Gilbert equations
• A convergent and precise finite element scheme for Landau-Lifschitz-Gilbert equation
• Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey spaces
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism
• A new finite element scheme for Landau-Lifschitz equations
• Existence, regularity and local uniqueness of the solutions to the Maxwell-Landau-Lifshitz system in three dimensions
• Existence and partial regularity results for the heat flow for harmonic maps
• The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
• Regular solutions for Landau-Lifschitz equation in a bounded domain.
• Higher order regularity results in 3D for the Landau-Lifshitz equation with an exchange field
• Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions
• On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness
• Partial regularity for two dimensional Landau-Lifshitz equations
• On Landau-Lifshitz’ equations for ferromagnetism
• The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error Estimates
• On a decoupled linear FEM integrator for eddy-current-LLG
• Existence of Partially Regular Solutions for Landau–Lifshitz Equations in ℝ³
• Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation
• Convergence of an Implicit Finite Element Method for the Landau–Lifshitz–Gilbert Equation

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