Heat flow with tangent penalisation converging to mean curvature motion

DOI10.1017/S0308210500021831zbMath0909.35069MaRDI QIDQ4212404

Jian Zhai

Publication date: 22 March 1999

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

local existence of classical solutionsglobal existence of the travelling wave solutionsLandau-Lifshitz equation of ferromagnetism

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Cites Work

• Motion of level sets by mean curvature. I
• On the evolution of harmonic mappings of Riemannian surfaces
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
• Harmonic maps of manifolds with boundary
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
• Fast Reaction, Slow Diffusion, and Curve Shortening
• Reaction-Diffusion Processes and Evolution to Harmonic Maps
• User’s guide to viscosity solutions of second order partial differential equations
• Phase transitions and generalized motion by mean curvature
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

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