On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities
A Guide to Theory, Applications, and Some Open Problems
Series: Progress in Nonlinear Differential Equations and Their Applications; 104;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 31 December 2024
- Number of Volumes 1 pieces, Book
- ISBN 9783031493737
- Binding Paperback
- See also 9783031493706
- No. of pages573 pages
- Size 235x155 mm
- Language English
- Illustrations XXIV, 573 p. 567
Categories
Long description:
Table of Contents:
"
General Introduction.- Basic Continuous Framework and Classical Assumptions Revisited.- Part I: A Toolbox for Discontinuous Hamilton-Jacobi Equations and Control Problems.- PDE Tools.- Control Tools.- Mixed Tools.- Other Tools.- Part II: Deterministic Control Problems and Hamilton-Jacobi Equations for Codimension One Discontinuities.- Introduction: Ishii Solutions for the Hyperplane Case.- The Control Problem and the ""Natural"" Value Function.- A Less Natural Value-Function, Regular and Singular Dynamics.- Uniqueness and Non-Uniqueness Features.- Adding a Specific Problem on the Interface.- Remarks on the Uniqueness Proofs, Problems without Controllability.- Further Discussions and Open Problems.- Part III: Hamilton-Jacobi Equations with Codimension One Discontinuities: The ""Network"" Point of View.- Introduction.- Flux-Limited Solutions for Control Problems and Quasi-Convex Hamiltonians.- Junction Viscosity Solutions.- From One Notion of Solution to the Others.- Applications and Emblematic Examples.- Further Discussions and Open Problems.- Part IV: General Discontinuities: Stratified Problems.- Stratified Solutions.- Connections with Control Problems and Ishii Solutions.- Stability Results.- Applications.- Further Discussions and Open Problems.- Part V: State-Constraint Problems.- Introduction to State-Constraint Problems.- Stratified Solutions for State-Constraint Problems.- Classical Boundary Conditions and Stratified Formulation.- Stability for Singular Boundary Value Problems.- Further Discussions and Open Problems.- Part VI: Investigating Other Applications.- KPP-Type Problems with Discontinuities.- And What about Jumps? And What about Networks.- Further Discussions and Open Problems.- Part VII: Appendices.- Notations and Terminology.- Assumptions, Hypotheses, Notions of Solutions.
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