Curvature effect on asymptotic profiles of spiral curves

Je Chiang Tsai, Zhengyang Zhang*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

We study the shape of spiral curves in an annulus which is governed by curvature flow equations with a driving force term. We establish that as the model parameter μ (which is the coefficient of the curvature) approaches ∞, the profile of the spiral curve tends to a line segment, while as μ approaches 0+, the limiting profile of the spiral curve is the involute of the inner circle of the annulus and the associated limiting rotational speed is the ratio of a constant c, which is the propagation speed of the planar wave, to the inner radius of the annulus. Hence the model parameter μ can be viewed as a twisted parameter. Finally, the spiral curve under consideration is shown to be with sign-changing curvature and exponentially stable.

原文英語
文章編號132657
期刊Physica D: Nonlinear Phenomena
413
DOIs
出版狀態已發佈 - 2020 12月
對外發佈

ASJC Scopus subject areas

  • 統計與非線性物理學
  • 數學物理學
  • 凝聚態物理學
  • 應用數學

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