On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities A Guide to Theory, Applications, and Some Open Problems /
This monograph presents the most recent developments in the study of Hamilton-Jacobi equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratifi...
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| Автори: | , |
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| Співавтор: | |
| Формат: | Електронний ресурс eКнига |
| Мова: | Англійська |
| Опубліковано: |
Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2024.
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| Редагування: | 1st ed. 2024. |
| Серія: | PNLDE Subseries in Control,
104 |
| Предмети: | |
| Онлайн доступ: | https://doi.org/10.1007/978-3-031-49371-3 |
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Зміст:
- 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.