UID:
almahu_9947366293702882
Format:
1 online resource (161 p.)
ISBN:
1-282-28951-9
,
9786612289514
,
0-08-095640-8
Series Statement:
Mathematics in science & engineering ; v. 131
Content:
Hamilton-Jacobi Equation: A Global Approach
Note:
Description based upon print version of record.
,
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 Solutions2. 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 Theory3. 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
,
English
Additional Edition:
ISBN 0-12-089350-9
Language:
English
