On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities - Guy Barles, Emmanuel Chasseigne

Blick ins Buch

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities (eBook)

A Guide to Theory, Applications, and Some Open Problems

Guy Barles, Emmanuel Chasseigne (Autoren)

eBook Download: PDF

2023 | 1st ed. 2024
XXIV, 573 Seiten
Springer Nature Switzerland (Verlag)
978-3-031-49371-3 (ISBN)

Lese- und Medienproben

Ebook-Leseprobe (PDF)

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 stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text.

After an initial section that provides a 'toolbox' containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text - such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization - and several key open problems are presented.

This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi Equations, network problems, or scalar conservation laws.

Guy Barles is a former professor at the University of Tours (1990-2021). During his career, his main research theme was nonlinear elliptic and parabolic equations, and in particular Hamilton-Jacobi and nonlocal equations. His main contributions concern various asymptotic problems including Large Deviations, homogenization and rate of convergence for numerical schemes, as well as front propagation problems, optimal control and modelling. He is the author of more than 120 articles, proceedings and books, including an introduction in French to viscosity solutions for Hamilton-Jacobi Equations and deterministic control problems.

Emmanuel Chasseigne is Maître de Conférences at the University of Tours since 2001. His main research themes are nonlinear elliptic and parabolic equations, diffusion equations, Hamilton-Jacobi and nonlocal equations. His main contributions are related to qualitative properties of solutions, optimal initial data, asymptotic problems, and optimal control, representing a total of 40 articles.

Erscheint lt. Verlag	29.12.2023
Reihe/Serie	PNLDE Subseries in Control
	PNLDE Subseries in Control
	Progress in Nonlinear Differential Equations and Their Applications
	Progress in Nonlinear Differential Equations and Their Applications
Zusatzinfo	XXIV, 573 p.
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Comparison principles • Deterministic control problems • Hamilton-Jacobi Equations with discontinuities • initial-boundary value problems • stability • Stratified problems • Vanishing viscosity method • Viscosity Solutions
ISBN-10	3-031-49371-0 / 3031493710
ISBN-13	978-3-031-49371-3 / 9783031493713

Haben Sie eine Frage zum Produkt?

PDF (Wasserzeichen)
Größe: 6,3 MB

DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Print-Ausgabe

Buch | Hardcover

181,89 €