Global solutions of the Landau--Lifshitz--Baryakhtar equation
arXiv:2302.02556 · doi:10.1016/j.jde.2023.06.033
Abstract
The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes into account contributions from nonlocal damping and is valid at moderate temperature below the Curie temperature. Therefore, it is used to explain some discrepancies between the experimental observations and the known theories in various problems on magnonics and magnetic domain-wall dynamics. In this paper, the existence and uniqueness of global weak, strong, and regular solutions to LLBar equation are proven. Hölder continuity of the solution is also discussed.
title changed, existence & uniqueness of global weak and strong solutions are shown
References in corpus (1)
Cited by in corpus (7)
- Mixed finite element methods for the Landau--Lifshitz--Baryakhtar and the regularised Landau--Lifshitz--Bloch equations in micromagnetics
- The stochastic Landau--Lifshitz--Baryakhtar equation: Global solution and invariant measure
- The Landau--Lifshitz--Bloch equation with spin diffusion: Global strong solution and finite element approximation
- Stable -conforming finite element methods for a class of nonlinear fourth-order evolution equations
- Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations
- Error analysis of scalar auxiliary variable finite element methods for the Landau--Lifshitz--Bloch equation
- Numerical analysis of the Landau--Lifshitz--Bloch equation with spin-torques