BALLISTIC AND SUB-BALLISTIC MOTION OF INTERFACES IN A FIELD OF RANDOM OBSTACLES

• 成果类型: Article
• 署名作者: Dondl, Patrick W.; Scheutzow, Michael
• 署名单位: University of Freiburg; Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1279
• 发表日期: 2017
• 页码: 3189-3200
• 关键词: RANDOM-COEFFICIENTS; random-media; DYNAMICS

摘要

We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a d-dimensional lattice coupled by the discrete Laplacian. At each lattice point, the system is subject to a constant driving force and a random obstacle force impeding free propagation. The obstacle force depends on the current state of the solution, and thus renders the problem nonlinear. For independent and identically distributed obstacle strengths with an exponential moment, we prove ballistic propagation (i.e., propagation with a positive velocity) of the interface if the driving force is large enough. For a specific case of dependent obstacles, we show that no stationary solution exists, but still the propagation of the front is not ballistic.