Bifurcations of spherically asymmetric solutions to an evolution equation for curves

DOI10.4171/IFB/474zbMath1490.35082WikidataQ113692009 ScholiaQ113692009MaRDI QIDQ2141697

Takeo Sugai

Publication date: 25 May 2022

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

zbMATH Keywords

self-similar solutionslinearized stabilitycurve shortening flowbifurcation solutions

Mathematics Subject Classification ID

Free boundary problems for PDEs (35R35) Bifurcations in context of PDEs (35B32) Self-similar solutions to PDEs (35C06) Quasilinear parabolic equations with mean curvature operator (35K93)

Cites Work

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• Flow by mean curvature of convex surfaces into spheres
• Non-trivial self-similar extinction solutions for a 3D Hele-Shaw suction problem
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Bifurcation from simple eigenvalues
• The volume preserving mean curvature flow near spheres
• On a planar area-preserving curvature flow
• A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area
• Analytic semigroups and optimal regularity in parabolic problems

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