Abstract
Minimizing movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimizing movement scheme involves a temporal parameter τ and a spatial parameter with τ describing the time step and the frequency of the oscillations being proportional to 1/. The extreme cases of fast time scales τ â and slow time scales â τ have been investigated in [4]. In this paper, the intermediate (critical) case of finite ratio /τ > 0 is studied. It is shown that a pinning threshold exists, with initial data below the threshold being a fixed point of the dynamics. A characterization of the pinning threshold is given. For initial data above the pinning threshold, the equation and velocity describing the homogenized motion are determined.
Originalsprache | Englisch |
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Seiten (von - bis) | 719-737 |
Seitenumfang | 19 |
Fachzeitschrift | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Jahrgang | 149 |
Ausgabenummer | 3 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Juni 2019 |
Extern publiziert | Ja |