Stochastic homogenization of interfaces moving with changing sign velocity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Cionlaga, Adina¹  Souganidis, Panagiotis E.¹  Tran, Hung V.¹ 

[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA

关键词: Stochastic homogenization;    Hamilton-Jacobi equations;    Viscosity solutions;    Non-coercive Hamiltonian;    Random media;    Front propagation;   

DOI  :  10.1016/j.jde.2014.09.019

来源: Elsevier

【 摘 要 】

We are interested in the averaging behavior of interfaces moving in stationary ergodic environments with oscillatory normal velocity which changes sign. The problem can be reformulated as the homogenization of a Hamilton-Jacobi equation with a positively homogeneous of degree one non-coercive Hamiltonian. The periodic setting was studied earlier by Cardaliaguet, Lions and Souganidis (2009) [16]. Here we concentrate in the random media and show that the solutions of the oscillatory Hamilton-Jacobi equation converge in L-infinity-weak star 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free