English
Related papers

Related papers: On the random G equation with nonzero divergence

200 papers

We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet and Souganidis, who proved…

Analysis of PDEs · Mathematics 2021-11-12 William Cooperman

We consider discrete non-divergence form difference operators in a random environment and the corresponding process--the random walk in a balanced random environment in $\mathbb{Z}^d$ with a finite range of dependence. We first quantify the…

Probability · Mathematics 2022-09-30 Xiaoqin Guo , Jonathon Peterson , Hung V. Tran

We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…

Analysis of PDEs · Mathematics 2026-05-22 Xiaoqin Guo , Wenjia Jing , Hung Vinh Tran , Yuming Paul Zhang

We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…

Analysis of PDEs · Mathematics 2013-12-31 Scott N. Armstrong , Pierre Cardaliaguet

We study the homogenization of a $G$-equation which is advected by a divergence free stationary vector field in a general ergodic random environment. We prove that the averaged equation is an anisotropic deterministic G-equation and we give…

Optimization and Control · Mathematics 2011-10-11 Pierre Cardaliaguet , Panagiotis E. Souganidis

We prove stochastic homogenization for a class of non-convex and non-coercive first-order Hamilton-Jacobi equations in a finite-range-dependence environment for Hamiltonians that can be expressed by a max-min formula. Exploiting the…

Analysis of PDEs · Mathematics 2025-10-30 Andrea Davini , Raimundo Saona , Bruno Ziliotto

We prove homogenization for possibly degenerate viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$, where $G$ is a quasiconvex, locally Lipschitz function with superlinear growth, the potential $V(x,\omega)$…

Analysis of PDEs · Mathematics 2025-04-17 Andrea Davini

In this paper, we consider homogenization of the Landau-Lifshitz equation with a highly oscillatory material coefficient with period $\varepsilon$ modeling a ferromagnetic composite. We derive equations for the homogenized solution to the…

Analysis of PDEs · Mathematics 2020-12-24 Lena Leitenmaier , Olof Runborg

In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both for the solution and the free boundary for the…

Analysis of PDEs · Mathematics 2021-12-22 Gohar Aleksanyan , Tuomo Kuusi

We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$ for a wide class of stationary ergodic random media in one space dimension. The momentum part $G(p)$ of the Hamiltonian is a…

Analysis of PDEs · Mathematics 2023-03-14 Andrea Davini , Elena Kosygina , Atilla Yilmaz

In this paper we provide a rate of convergence for periodic homogenization of Hamilton-Jacobi-Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where the convexity plays a…

Analysis of PDEs · Mathematics 2020-12-08 Andrei Rodríguez-Paredes , Erwin Topp

We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is…

Analysis of PDEs · Mathematics 2010-11-02 James Nolen , Alexei Novikov

We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\Omega \times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where…

Analysis of PDEs · Mathematics 2023-04-14 Oleg Imanuvilov , Hongyu Liu , Masahiro Yamamoto

In a bounded domain $\Omega \subset \mathbb{R}^d$ over time interval $(0,T)$, we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian. We attach the non-zero Robin…

Analysis of PDEs · Mathematics 2023-07-11 Oleg Imanuvilov , Hongyu Liu , Masahiro Yamamoto

We prove stochastic homogenization for reaction-advection-diffusion equations with random space-time-dependent KPP reactions with temporal correlations that are decaying in an appropriate sense. We show that the limiting homogenized dynamic…

Analysis of PDEs · Mathematics 2022-03-03 Yuming Paul Zhang , Andrej Zlatos

This article establishes a stochastic homogenization result for the first order Hamilton-Jacobi equation on a Riemannian manifold $M$, in the context of a stationary ergodic random environment. The setting involves a finitely generated…

Analysis of PDEs · Mathematics 2025-10-14 Marco Pozza , Alfonso Sorrentino

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…

Statistics Theory · Mathematics 2021-05-24 Sara Kristin Schmidt , Max Wornowizki , Roland Fried , Herold Dehling

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…

Analysis of PDEs · Mathematics 2023-01-02 Hoang Nguyen-Tien

We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may…

Probability · Mathematics 2019-05-27 Julian Fischer

We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a…

Mathematical Physics · Physics 2017-09-19 Jeremiah Birrell , Jan Wehr
‹ Prev 1 2 3 10 Next ›