Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients
Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients
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具有无界随机系数的半线性抛物线界面模型中的正传播速度
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Scheutzow
中科院分区：
文献类型：
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作者：
P. Dondl;M. Scheutzow
我们考虑一个模型的传播驱动接口通过随机场的障碍。演化方程，通常被称为淬火爱德华-威尔金森模型，是一个半线性抛物方程，具有恒定的驱动项和随机非线性模型的障碍场的影响。对于孤立的障碍物为中心的格点和承认一个随机强度与指数尾巴的情况下，我们表明，界面传播的有限速度足够大的驱动力。证明包括一个离散化的发展方程和一个上鞅估计类似于分支随机游动的研究。
We consider a model for the propagation of a driven interface through a random field of obstacles. The evolution equation, commonly referred to as the Quenched Edwards-Wilkinson model, is a semilinear parabolic equation with a constant driving term and random nonlinearity to model the influence of the obstacle field. For the case of isolated obstacles centered on lattice points and admitting a random strength with exponential tails, we show that the interface propagates with a finite velocity for sufficiently large driving force. The proof consists of a discretization of the evolution equation and a supermartingale estimate akin to the study of branching random walks.