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Pinning of interfaces in random media. (English) Zbl 1231.35323
Summary: For a model for the propagation of a curvature sensitive interface in a time independent random medium, as well as for a linearized version which is commonly referred to as quenched Edwards-Wilkinson equation, we prove existence of a stationary positive supersolution at non-vanishing applied load. This leads to the emergence of a hysteresis that does not vanish for slow loading, even though the local evolution law is viscous (in particular, the velocity of the interface in the model is linear in the driving force).

35R60 PDEs with randomness, stochastic partial differential equations
74N20 Dynamics of phase boundaries in solids
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