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

Name: On Modern Approaches of Hamilton-Jacobi Equations: A Guide to Theory, Applications, and Some Open Problems
Brand: Birkhauser
SKU: 9783031493737
Price: 12354.0 INR
Availability: InStock

by Guy Barles , Emmanuel Chasseigne

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ISBN13: 9783031493737
Binding: Paperback
Subject: N/A
Publisher: Birkhauser
Publisher Imprint: Birkhauser
Publication Date: January 1, 2024
Pages: 600
Original Price: EUR 169.99
Language: English
Edition: N/A
Item Weight: 839 grams
BISAC Subject(s): Differential Equations / General

About The Book

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 Author

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.

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