Computational and qualitative aspects of motion of plane curves with a curvature adjusted tangential velocity

DOI10.1002/mma.2554zbMath1255.35148arXiv0711.2568OpenAlexW2067042508MaRDI QIDQ4649029

Shigetoshi Yazaki, Daniel Ševčovič

Publication date: 19 November 2012

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2568

zbMATH Keywords

flowing finite volume methodlocal existence of solutionsnonlocal geometric flowscurvature driven flowclosed Jordan curves

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Applications of global differential geometry to the sciences (53C80) Method of lines for boundary value problems involving PDEs (65N40)

Related Items (7)

An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow ⋮ Qualitative and Numerical Aspects of a Motion of a Family of Interacting Curves in Space ⋮ Area preserving geodesic curvature driven flow of closed curves on a surface ⋮ Evolution of plane curves with a curvature adjusted tangential velocity ⋮ Analysis of Kuramoto-Sivashinsky Model of Flame/Smoldering Front by Means of Curvature Driven Flow ⋮ Lagrangian evolution approach to surface-patch quadrangulation. ⋮ Towards modelling spiral motion of open plane curves

Cites Work

• Unnamed Item
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• An isoperimetric inequality with applications to curve shortening
• On a non-local curve evolution problem in the plane
• Semigroups of linear operators and applications to partial differential equations
• The heat equation shrinking convex plane curves
• Parabolic equations for curves on surfaces. I: Curves with \(p\)-integrable curvature
• Axioms and fundamental equations of image processing
• Accurate numerical scheme for the flow by curvature
• On affine plane curve evolution
• Removing the stiffness from interfacial flows with surface tension
• Weak solutions of the curve shortening flow
• Evolution of Plane Curves Driven by a Nonlinear Function of Curvature and Anisotropy
• A Higher Order Scheme for a Tangentially Stabilized Plane Curve Shortening Flow with a Driving Force
• Nonlinear analytic semiflows
• CONVERGENCE OF A SEMI-DISCRETE SCHEME FOR THE CURVE SHORTENING FLOW
• On the affine heat equation for non-convex curves
• A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
• Convergence of a Crystalline Algorithm for the Motion of a Closed Convex Curve by a Power of Curvature $V=K^\alpha$

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