## Abstract

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.

Original language | English |
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Article number | 132657 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 413 |

DOIs | |

Publication status | Published - 2020 Dec |

Externally published | Yes |

## Keywords

- Asymptotic profiles
- Curvature flow equation
- Involute of circles
- Steadily rotating spiral curve

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics