On Modern Approaches of Hamilton-Jacobi Equations and Control Probl...
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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

Guy Barles, Emmanuel Chasseigne


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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.

About the book
Author
Guy  Barles , Emmanuel  Chasseigne
Imprint
Birkhäuser
Collection
Progress in Nonlinear Differential Equations and Their Applications
Publication date
2023-12-29
Pages
573 pages
Print ISBN
9783031493706
Language
English
Ebook informations
EAN PDF
9783031493713
Price
£149.50
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Copy count 5
Print count 57
File size 6287 Ko
Ce livre est accessible aux handicaps   Informations accessibility
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