局部干摩擦导致的界面钉扎
Pinning of Interfaces by Localized Dry Friction
摘要：
我们考虑了一个由抛物型方程控制的非均匀环境中界面演化的模型。引入的异质性作为施加局部干摩擦的障碍。我们的主要结果建立了适当的随机分布的障碍，即，界面被障碍物钉扎，直到超过某一临界的施加驱动力。在钉扎和去钉扎的背景下处理这样一个模型需要一个比较原则。我们证明了这一性质，从而存在的黏性解。此外，在合理的假设下，我们证明了黏性解等价于弱解。
英文摘要：
We consider a model for the evolution of an interface in a heterogeneous environment governed by a parabolic equation. The heterogeneity is introduced as obstacles exerting a localized dry friction. Our main result establishes the emergence of a rate-independent hysteresis for suitable randomly distributed obstacles, i.e., interfaces are pinned by the obstacles until a certain critical applied driving force is exceeded. The treatment of such a model in the context of pinning and depinning requires a comparison principle. We prove this property and hence the existence of viscosity solutions. Moreover, under reasonable assumptions, we show that viscosity solutions are equivalent to weak solutions.
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