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On modern approaches of Hamilton-jacobi equations and control problems with discontinuitiesa guide to theory, applications, and some open problems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	On modern approaches of Hamilton-jacobi equations and control problems with discontinuitiesby Guy Barles, Emmanuel Chasseigne.
Reminder of title:	a guide to theory, applications, and some open problems /
Author:	Barles, Guy.
other author:	Chasseigne, Emmanuel.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xxiv, 573 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Hamilton-Jacobi equations.
Online resource:	https://doi.org/10.1007/978-3-031-49371-3
ISBN:	9783031493713$q(electronic bk.)

On modern approaches of Hamilton-jacobi equations and control problems with discontinuitiesa guide to theory, applications, and some open problems /
Barles, Guy.

On modern approaches of Hamilton-jacobi equations and control problems with discontinuitiesa guide to theory, applications, and some open problems /[electronic resource] :by Guy Barles, Emmanuel Chasseigne. - Cham :Springer Nature Switzerland :2024. - xxiv, 573 p. :ill., digital ;24 cm. - PNLDE subseries in control,v. 1042731-7374 ;. - PNLDE subseries in control ;v. 98..

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.

ISBN: 9783031493713$q(electronic bk.)

Standard No.: 10.1007/978-3-031-49371-3doiSubjects--Topical Terms:

275723
Hamilton-Jacobi equations.

LC Class. No.: QA378

Dewey Class. No.: 515.353

On modern approaches of Hamilton-jacobi equations and control problems with discontinuitiesa guide to theory, applications, and some open problems /
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505 0 $a 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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