Stochastic homogenization of front propagation problem with unbounded velocity
Hajej, Ahmed (2017), Stochastic homogenization of front propagation problem with unbounded velocity, Journal of Differential Equations, 262, 7, p. 3805-3836. 10.1016/j.jde.2016.10.035
TypeArticle accepté pour publication ou publié
Journal nameJournal of Differential Equations
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Abstract (EN)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.
Subjects / KeywordsStochastic homogenization; Unbounded Hamilton–Jacobi equation; Viscosity solutions; Finite range of dependence; First passage in percolation; Front propagation
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