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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 /
  • 紀錄類型: 書目-電子資源 : Monograph/item
    正題名/作者: On modern approaches of Hamilton-jacobi equations and control problems with discontinuities/ by Guy Barles, Emmanuel Chasseigne.
    其他題名: a guide to theory, applications, and some open problems /
    作者: Barles, Guy.
    其他作者: Chasseigne, Emmanuel.
    出版者: Cham :Springer Nature Switzerland : : 2024.,
    面頁冊數: xxiv, 573 p. :ill., digital ;24 cm.
    內容註: 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.
    Contained By: Springer Nature eBook
    標題: Hamilton-Jacobi equations. -
    電子資源: https://doi.org/10.1007/978-3-031-49371-3
    ISBN: 9783031493713
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