The Hamilton-Jacobi Equation
A Global Approach
Erschienen am 14. Mai 2014
161 Seiten
978-0-08-095640-4 (ISBN)
Beschreibung
Hamilton-Jacobi Equation: A Global Approach
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Inhalt
- Front Cover
- The Hamilton-Jacobi Equation: A Global Approach
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Introduction
- Chapter I. Classical Methods
- Prefatory Remarks
- 1. Exact Equations and Direct Integration
- 2. The General Solution
- 3. Separation of Variables
- 4. Characteristics and Integral Surfaces
- 5. The Complete Integral
- 6. The Cauchy-Kowaleski Theorem
- 7. The Legendre Transform
- 8. Characteristic Theory
- 9. Elementary Transformations
- 10. Variational Methods
- 11. Hamilton-Jacobi Theory
- 12. Contact Transformations
- 13. Similarity Methods
- Chapter II. Existence
- 1. Global Solutions
- 2. The Compatibility Condition
- 3. The Variational Solution
- 4. Growth Conditions
- 5. Regularity
- 6. Space-Time Independent Hamiltonians
- 7. Space-Time Dependence
- 8. Equivalent Problems
- 9. A Little u Dependence?
- 10. Other Existence Techniques
- Chapter III. Uniqueness and Properties of Solutions
- Preamble
- 1. Basic Inequalities
- 2. Uniqueness for the Cauchy Problem
- 3. Uniqueness for More General Boundaries
- 4. Maximality of the Variational Solution
- Chapter IV. Applications and Numerical Methods
- General Comments
- 1. Some Physical Applications
- 2. Applications in the Calculus of Variations and Control Theory
- 3. Minimization of a Function
- 4. Quasilinear Equations
- 5. Numerical Methods for the Calculus of Variations
- 6. Numerical Methods for First-Order Equations
- 7. Artificial Viscosity
- Bibliography
- Index
