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arXiv · 1909.04717

Pinning of Interfaces by Localized Dry Friction

Luca Courte·Patrick Dondl·Ulisse Stefanelli
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Abstract

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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Luca Courte, Patrick Dondl, Ulisse Stefanelli. 2019-09-10. Pinning of Interfaces by Localized Dry Friction. https://arxiv.org/abs/1909.04717

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