Related papers: Homogenization of the Landau-Lifshitz equation

The full Landau-Lifshitz-Gilbert equation with periodic material coefficients and natural boundary condition is employed to model the magnetization dynamics in composite ferromagnets. In this work, we establish the convergence between the…

In this paper, we consider several possible ways to set up Heterogeneous Multiscale Methods for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, which can be seen as a means to modeling rapidly varying…

We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…

We study the rate of convergence in periodic homogenization for convex Hamilton--Jacobi equations with multiscales, where the Hamiltonian $H=H(x, y, p): \mathbb{R}^n \times \mathbb{T}^n \times \mathbb{R}^n \to \mathbb{R }$ depends on both…

We study the rate of convergence of $u^\epsilon$, as $\epsilon \to 0+$, to $u$ in periodic homogenization of Hamilton-Jacobi equations. Here, $u^\epsilon$ and $u$ are viscosity solutions to the oscillatory Hamilton-Jacobi equation and its…

We study the optimal convergence rate for homogenization problem of convex Hamilton-Jacobi equations when the Hamitonian is periodic with respect to spatial and time variables, and notably time-dependent. We prove a result similar to that…

This paper considers a family of second-order periodic parabolic equations with highly oscillating potentials, which have been considered many times for the time-varying potentials in stochastic homogenization. Following a standard…

Ferromagnetic materials tend to develop very complex magnetization patterns whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert equation (LLG). In this paper, we construct time-periodic solutions for LLG in the regime…

We study the optimal rate of convergence in periodic homogenization of the viscous Hamilton-Jacobi equation $u^\varepsilon_t + H(\frac{x}{\varepsilon},Du^\varepsilon) = \varepsilon \Delta u^\varepsilon$ in $\mathbb R^n\times (0,\infty)$…

This paper is concerned with the optimal convergence rate in homogenization of higher order parabolic systems with bounded measurable, rapidly oscillating periodic coefficients. The sharp $O(\va)$ convergence rate in the space $L^2(0,T;…

This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…

This paper is devoted to the homogenization of Shr\"odinger type equations with periodically oscillating coefficients of the diffusion term, and a rapidly oscillating periodic time-dependent potential. One convergence theorem is proved and…

We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…

The dynamics of magnetisation in a bounded ferromagnet in $\mathbb{R}^d$ ($d=1,2$) at high temperatures can be described by the stochastic Landau--Lifshitz--Bloch (sLLB) equation, which is a vector-valued quasilinear stochastic partial…

In this paper, we show that the rate of convergence in periodic homogenization of convex Hamilton-Jacobi equations is always $O(\varepsilon)$, which is optimal. This is a natural extension of a result concerning stable norms in metric…

This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…

In this paper, we find some error estimates for periodic homogenization of p-Laplace type equations under the same structure assumption on homogenized equations. The main idea is that by adjusting the size of the difference quotient of the…

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a…

We investigate in this work the rate of convergence to equilibrium of solutions to the spatially homogeneous Landau equation with soft potentials. Firstly, we prove a polynomial in time convergence using an entropy method with some new a…

Here, we study the periodic homogenization problem of nonlinear weakly coupled systems of Hamilton-Jacobi equations in the convex setting. We establish a rate of convergence $O(\sqrt{\varepsilon})$ which is sharp.