TY - JOUR

T1 - Curvature effect on asymptotic profiles of spiral curves

AU - Tsai, Je Chiang

AU - Zhang, Zhengyang

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - Asymptotic profiles

KW - Curvature flow equation

KW - Involute of circles

KW - Steadily rotating spiral curve

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U2 - 10.1016/j.physd.2020.132657

DO - 10.1016/j.physd.2020.132657

M3 - Article

AN - SCOPUS:85088861669

SN - 0167-2789

VL - 413

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

M1 - 132657

ER -