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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 consider the homogenization of monotone systems of viscous Hamilton-Jacobi equations with convex nonlinearities set in the stationary, ergodic setting. The primary focus of this paper is on collapsing systems which, as the microscopic…

Analysis of PDEs · Mathematics 2012-05-09 Benjamin J. Fehrman

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

We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes…

Analysis of PDEs · Mathematics 2026-05-22 Seho Park

We prove stochastic homogenization for a general class of coercive, nonconvex Hamilton-Jacobi equations in one space dimension. Some properties of the effective Hamiltonian arising in the nonconvex case are also discussed.

Analysis of PDEs · Mathematics 2014-10-28 S. N. Armstrong , H. V. Tran , Y. Yu

We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered…

Analysis of PDEs · Mathematics 2020-05-05 Nicolas Forcadel , Fayad Rim , Ibrahim Hassan

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 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…

Analysis of PDEs · Mathematics 2025-11-03 Yuxi Han , Son Tu

We study homogenization for a class of stationnary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a…

Analysis of PDEs · Mathematics 2022-11-30 Yves Achdou , Claude Le Bris

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

In this paper, we will prove the random homogenization of general coercive non-convex Hamilton-Jacobi equations in one dimensional case. This extends the result of Armstrong, Tran and Yu when the Hamiltonian has a separable form…

Analysis of PDEs · Mathematics 2015-07-28 Hongwei Gao

We provide an example of a Hamilton-Jacobi equation in which stochastic homogenization does not occur. The Hamiltonian involved in this example satisfies the standard assumptions of the literature, except that it is not convex.

Analysis of PDEs · Mathematics 2020-07-09 Bruno Ziliotto

This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…

Analysis of PDEs · Mathematics 2013-03-11 Cyril Imbert , Régis Monneau , Hasnaa Zidani

In this paper, we consider first order Hamilton-Jacobi (HJ) equations posed on a ``junction'', that is to say the union of a finite number of half-lines with a unique common point. For this continuous HJ problem, we propose a finite…

Numerical Analysis · Mathematics 2013-06-04 Guillaume Costeseque , Jean-Patrick Lebacque , Régis Monneau

We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…

Numerical Analysis · Mathematics 2010-08-06 Matthew Dobson , Claude Le Bris , Frederic Legoll

This paper is the first attempt to systematically study properties of the effective Hamiltonian $\overline{H}$ arising in the periodic homogenization of some coercive but nonconvex Hamilton-Jacobi equations. Firstly, we introduce a new and…

Analysis of PDEs · Mathematics 2017-01-05 Jianliang Qian , Hung V. Tran , Yifeng Yu

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…

Analysis of PDEs · Mathematics 2010-02-10 Fabio Camilli , Olivier Ley , Paola Loreti

We prove, under some assumptions, the existence of correctors for the stochastic homoge-nization of of " viscous " possibly degenerate Hamilton-Jacobi equations in stationary ergodic media. The general claim is that, assuming knowledge of…

Analysis of PDEs · Mathematics 2017-04-26 Pierre Cardaliaguet , Panagiotis Souganidis

In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of integro-differential type. We consider the case when the fractional diffusion has the same order as the…

Analysis of PDEs · Mathematics 2020-02-24 Adina Ciomaga , Daria Ghilli , Erwin Topp

We establish homogenization for nondegenerate viscous Hamilton-Jacobi equations in one space dimension when the diffusion coefficient $a(x,\omega) > 0$ and the Hamiltonian $H(p,x,\omega)$ are general stationary ergodic processes in $x$. Our…

Analysis of PDEs · Mathematics 2024-03-26 Elena Kosygina , Atilla Yilmaz