Curve diffusion and straightening flows on parallel lines

2017/03/30 by Wheeler, Glen, Wheeler, Valentina-Mira · 2 citations
#53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.10711

Abstract

In this paper, we study families of immersed curves γ:(-1,1)×[0,T)→ℝ² with free boundary supported on parallel lines \η₁, η₂\:ℝ→ℝ² evolving by the curve diffusion flow and the curve straightening flow. The evolving curves are orthogonal to the boundary and satisfy a no-flux condition. We give estimates and monotonicity on the normalised oscillation of curvature, yielding global results for the flows.

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