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The paper entitled "Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature" by T Ilmanen constructs Brakke's motion from Allen-Cahn equation, which is one of the measure theoretic approaches to motion by mean curvature.
This book first proposes a new idea that involves a new equation of the Allen-Cahn type to construct Brakke's motion; secondly explaining how to construct it through Ilmanen's approach as easily as possible.
Contents:
- Introduction
- Mean Curvature Flow
- Approximation of Mean Curvature Flow
- New Partial Differential Equations of Allen-Cahn Type
- Ilmanen's Approach to Construct Brakke's Motion
- Appendices:
- Preparation on ODE and PDE
- Background on the Geometric Measure Theory
Readership: Researchers in calculus of variations and optimal control, partial differential equations, ordinary differential equations, integral equations, differential geometry.
