Stochastic homogenization of a front propagation problem with unbounded velocity

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• 作者：A. Hajej ^{hajej@ceremade.dauphine.fr}
• 关键词：35B27 ; 35F21 ; 49L25 ; 93E20 ; 78A48 ; 60K35
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 April 2017
• 年：2017
• 卷：262
• 期：7
• 页码：3805-3836
• 全文大小：450 K
• 卷排序：262

文摘

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.