Pinning and de-pinning phenomena in front propagation in heterogeneous media
Pinning and de-pinning phenomena in front propagation in heterogeneous media
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异质介质中前向传播的钉扎和脱钉现象
DOI：
10.4171/ifb/136
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发表时间：
2006
影响因子：
1
通讯作者：
N. Yip
中科院分区：
文献类型：
--
作者：
N. Dirr;N. Yip
本文研究了在外部驱动力F和底层非均质环境共同作用下，在模拟材料相界扩展过程中出现的一些演化偏微分方程的钉住和去钉住现象。现象学是固定状态的存在——固定解——对于小的F值，以及当F超过某个阈值时真实运动的出现。在周期性介质的情况下，我们在过渡区附近定量地描述了界面速度的标度行为作为F的函数。对一类半线性反应扩散方程证明了上述结果。
This paper investigates the pinning and de-pinning phenomena of some evolutionary partial differential equations which arise in the modelling of the propagation of phase boundaries in materials under the combined effects of an external driving force F and an underlying heterogeneous environment. The phenomenology is the existence of pinning states—stationary solutions—for small values of F, and the appearance of genuine motion whenF is above some threshold value. In the case of a periodic medium, we characterise quantitatively, near the transition regime, the scaling behaviour of the interface velocity as a function of F . The results are proved for a class of semilinear and reaction-diffusion equations.