Theory and numerics for Chen's flow of curves

نویسندگان

چکیده

In this article we study Chen's flow of curves from theoretical and numerical perspectives. We investigate two settings: that closed immersed ω-circles, lines satisfying a cocompactness condition. each the settings our goal is to find geometric conditions allow us understand global behaviour flow: for cocompact case, condition straightforward argument largely standard. For case however, quite complex. The shrinks every initial curve point if it does not become singular beforehand, must identify ensure as well in order perform requisite rescaling. are able successfully conduct full analysis rescaling under curvature resembles mean more than other fourth-order such elastic or diffusion flow, despite lack maximum comparison principles. Our work informed by include section explains algorithms used.

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ژورنال

عنوان ژورنال: Journal of Differential Equations

سال: 2023

ISSN: ['1090-2732', '0022-0396']

DOI: https://doi.org/10.1016/j.jde.2023.02.064