Research Catalog

Title

Generalized solutions of first-order PDEs : the dynamical optimization perspective / Andreĭ I. Subbotin.

Author

Subbotin, A. I. (Andreĭ Izmaĭlovich)

Publication

Boston : Birkhäuser, [1995], ©1995.

Items in the Library & Off-site

Holdings

Details

Description

xi, 312 pages : illustrations; 25 cm.

Series Statement

Systems & control

Uniform Title

Systems & control.

Subject

• Differential equations, Partial > Numerical solutions
• Equations aux dérivées partielles > Solutions numériques

Bibliography (note)

• Includes bibliographical references (p. [291]-310) and index.

Contents

• I. Generalized Characteristics of First-Order PDE's. 1. The Classical Method of Characteristics. 2. Characteristic Inclusions. 3. Upper and Lower Semicontinuous Solutions. 4. Criteria of Weak Invariance for Minimax Solutions. 5. Piecewise Smooth Solutions -- II. Cauchy Problems for Hamilton-Jacobi Equations. 6. Minimax Solutions of Hamilton-Jacobi Equations. 7. Uniqueness of Minimax Solution of Cauchy Problem for Hamilton-Jacobi Equation. 8. Existence of Minimax Solution of Cauchy Problem for Hamilton-Jacobi Equation. 9. Uniqueness under Weakened Assumptions. 10. Constructive and Numerical Methods -- III. Differential Games. 11. Basic Notions of the Theory of Differential Games. 12. Proof of Existence of Value Function of Differential Game. 13. Stable Bridges and Extremal Strategies. 14. Some Remarks. 15. Mixed Feedback Strategies and Counter-Strategies. 16. Constructive and Numerical Methods of the Theory of Differential Games -- IV. Boundary-Value Problems for First-Order PDE's.
• 17. Cauchy Problems for Hamilton Jacobi Equations with Additional Conditions in the Form of Inequalities. 18. Discontinuous Solutions of Dirichlet-Type Boundary-Value Problem. 19. Time-Optimal Differential Games. 20. Piecewise-Linear Approximations to Minimax Solutions of Hamilton Jacobi Equations -- App. A1 Justification of the Classical Method of Characteristics -- App. A2 Multifunctions -- App. A3 Semicontinuous Functions -- App. A4 Convex Functions -- App. A5 Contingent Tangent Cones, Directional Derivatives, Subdifferentials -- App. A6 On a Property of Subdifferentials -- App. A7 Differential Inclusions -- App. A8 Criteria for Weak Invariance.

ISBN

• 0817637400 (acid-free paper)
• 3764337400 (acid-free paper)

LCCN

94037167

OCLC

ocm31331559

Owning Institutions

Columbia University Libraries