Surface Evolution Equations: A Level Set Approach - Yoshikazu Giga
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This book presents a self-contained introduction to the analytic foundation of a level set method for various surface evolution equations including curvature flow equations. These equations are important for many fields of applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the in ... Full description
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Description
This book presents a self-contained introduction to the analytic foundation of a level set method for various surface evolution equations including curvature flow equations. These equations are important for many fields of applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set method. TOC:Introduction.- Surface Evolution Equations.- Viscosity Solutions.- Comparison Principle.- Classical Level Set Method.- Set-theoretic Approach.- Bibliography.- Index.
More Information
| Author | Yoshikazu Giga |
|---|---|
| Publisher | Birkhäuser Basel |
| Release year | 2006 |
| Cover type | Hardcover |
| EAN | 9783764324308 |