Stochastic homogenization of interfaces moving with changing sign velocity

2014/04/01 by Adina Ciomaga, Panagiotis E. Souganidis, Ciomaga, A. +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1404.0364

openalex publication_date 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in the averaged behavior of interfaces moving in stationary ergodic environments, with oscillatory normal velocity which changes sign. This problem can be reformulated, using level sets, as the homogenization of a Hamilton-Jacobi equation with a positively homogeneous non-coercive Hamiltonian. The periodic setting was earlier studied by Cardaliaguet, Lions and Souganidis (2009). Here we concentrate in the random media and show that the solutions of the oscillatory Hamilton-Jacobi equation converge in L^∞-weak * to a linear combination of the initial datum and the solutions of several initial value problems with deterministic effective Hamiltonian(s), determined by the properties of the random media.

Citations

• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Stochastic homogenization of a nonconvex Hamilton-Jacobi equation

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