Stochastic homogenization of a front propagation problem with unbounded velocity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Hajej, A.¹ 

[1] Univ Paris 09, CEREMADE, Pl Du Marechal De Lattre De Tassigny, F-75775 Paris 16, France

关键词: Stochastic homogenization;    Unbounded-Hamilton Jacobi equation;    Viscosity solutions;    Finite range of dependence;    First passage in percolation;    Front propagation;   

DOI  :  10.1016/j.jde.2016.10.035

来源: Elsevier

【 摘 要 】

We study the homogenization of Hamilton Jacobi equations which arise in front propagation problems in stationary ergodic media. Our results are obtained for fronts moving with possible unbounded velocity. We show, by an example, that the homogenized Hamiltonian, which always exists, may be unbounded. In this context, we show convergence results if we start with a compact initial front. On the other hand, if the media satisfies a finite range of dependence condition, we prove that the effective Hamiltonian is bounded and obtain classical homogenization in this context. (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free