The Hamilton-Jacobi equation : a global approach / Stanley H. Benton, Jr.

Format:

Book

Author/Creator:

Benton, Stanley H.

Series:

Mathematics in Science and Engineering

Mathematics in science & engineering ; v. 131

Language:

English

Subjects (All):

Hamilton-Jacobi equations.

Calculus of variations.

Physical Description:

1 online resource (161 p.)

Place of Publication:

New York : Academic Press, 1977.

Language Note:

English

Summary:

Hamilton-Jacobi Equation: A Global Approach

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28951-9

9786612289514

0-08-095640-8

OCLC:

316568233