Shape of spirals

DOI10.2748/tmj/1178224973zbMath0915.35048OpenAlexW2039529850MaRDI QIDQ1273494

Naoyuki Ishimura

Publication date: 7 December 1998

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178224973

zbMATH Keywords

curve shortening equationevolution of planar curves by curvaturespiral-like self-similar solutions

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Curves in Euclidean and related spaces (53A04) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (5)

On the structure of steady solutions for the kinematic model of spiral waves in excitable media ⋮ A crystalline motion of spiral-shaped curves with symmetry ⋮ Curvature effect on asymptotic profiles of spiral curves ⋮ Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion ⋮ A level set approach reflecting sheet structure with single auxiliary function for evolving spirals on crystal surfaces

Cites Work

• On the formation of singularities in the curve shortening flow
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• Singular perturbation theory of traveling waves in excitable media (A review)
• Singularities of the curve shrinking flow for space curves
• Limit shape of the cross-section of shrinking doughnuts
• Complex dynamics of spiral waves and motion of curves
• Evolving graphs by singular weighted curvature
• Existence of selfsimilar shrinking curves for anisotropic curvature flow equations
• Curvature evolution of plane curves with prescribed opening angle

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