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

Barles, Guy, Chasseigne, Emmanuel

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities: A Guide to Theory, Applications, and Some Open Problems
  • 出版商: Birkhauser Boston
  • 出版日期: 2023-12-30
  • 售價: $7,620
  • 貴賓價: 9.5 折 $7,239
  • 語言: 英文
  • 頁數: 573
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031493702
  • ISBN-13: 9783031493706

    • 下單後立即進貨 (約1週~2週)

商品描述

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.

商品描述(中文翻譯)

這本專著介紹了哈密爾頓-雅可比方程和具有不連續性的控制問題的最新發展，主要從偏微分方程的角度來探討。詳細研究了兩個主要情況：維數為1的不連續性情況和分層情況，其中不連續性可以是任意維數。在這兩種情況下，與確定性控制問題的聯繫被仔細研究，並且整本書中都有大量的例子和應用。

在一個提供了關鍵結果的“工具箱”部分之後，第二部分和第三部分完整地描述了幾種最近引入的方法，用於處理涉及維數為1的不連續性或網絡的問題。其餘部分涉及整個空間R^N或具有狀態約束的有界或無界域中的分層問題。特別是，使用分層解來處理具有邊界條件的問題，其中邊界可能是非光滑的，數據可能存在不連續性。整本書探討了許多具體問題的應用，例如科爾莫戈羅夫-彼得羅夫斯基-皮斯庫諾夫（KPP）類型問題，大偏差，水平集方法，大時間行為和均質化，並提出了一些關鍵的未解決問題。

這本專著對於從事確定性控制問題和哈密爾頓-雅可比方程、網絡問題或標量守恆定律的研究生和研究人員具有興趣。

作者簡介

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.

作者簡介(中文翻譯)

Guy Barles是圖爾大學（1990-2021）的前教授。在他的職業生涯中，他的主要研究主題是非線性橢圓和抛物方程，特別是Hamilton-Jacobi和非局部方程。他的主要貢獻涉及各種漸近問題，包括大偏差、均質化和數值方案的收斂速度，以及前沿傳播問題、最優控制和建模。他是120多篇文章、會議記錄和書籍的作者，其中包括一本介紹Hamilton-Jacobi方程和確定性控制問題的法文入門書。

Emmanuel Chasseigne自2001年起擔任圖爾大學的Maître de Conférences。他的主要研究主題是非線性橢圓和抛物方程、擴散方程、Hamilton-Jacobi和非局部方程。他的主要貢獻與解的定性特性、最優初始數據、漸近問題和最優控制有關，共發表了40篇文章。

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