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Produktbild: On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities
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On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities A Guide to Theory, Applications, and Some Open Problems

Aus der Reihe PNLDE Subseries in Control
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159,99 € UVP 181,89 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

30.12.2023

Abbildungen

XXIV, 573 p.

Verlag

Springer

Seitenzahl

573

Maße (L/B/H)

24,1/16/3,8 cm

Gewicht

1057 g

Auflage

1st edition 2024

Sprache

Englisch

ISBN

978-3-031-49370-6

Beschreibung

Rezension

“The monograph is ambitious in scope, spanning around 600 pages, and is structured around six central parts. Each part plays a distinct role, gradually leading the reader from fundamental tools to advanced topics. ... This book succeeds in its ambitious mission: to create a comprehensive, evolving framework for Hamilton-Jacobi equations with discontinuities. ... The text is mathematically demanding, but it rewards the reader with deep insights, careful proofs, and a wealth of applications.” (Alpár R. Mészáros, zbMATH 1573.35001, 2026) 


“The monograph provides comprehensive, long, and self-contained descriptions and analyses of such problems and can be used for a one semester course at the graduate or advanced undergraduate level.” (Giuseppe Maria Coclite, Mathematical Reviews, June, 2025)

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

30.12.2023

Abbildungen

XXIV, 573 p.

Verlag

Springer

Seitenzahl

573

Maße (L/B/H)

24,1/16/3,8 cm

Gewicht

1057 g

Auflage

1st edition 2024

Sprache

Englisch

ISBN

978-3-031-49370-6

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: ProductSafety@springernature.com

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  • Produktbild: On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

  • 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.