LEADER 06007nam 22006975 450 001 9910799203803321 005 20241007113255.0 010 $a3-031-49371-0 024 7 $a10.1007/978-3-031-49371-3 035 $a(MiAaPQ)EBC31051293 035 $a(Au-PeEL)EBL31051293 035 $a(DE-He213)978-3-031-49371-3 035 $a(CKB)29510231800041 035 $a(EXLCZ)9929510231800041 100 $a20231229d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOn Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities $eA Guide to Theory, Applications, and Some Open Problems /$fby Guy Barles, Emmanuel Chasseigne 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (569 pages) 225 1 $aPNLDE Subseries in Control,$x2731-7374 ;$v104 311 08$aPrint version: Barles, Guy On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities Cham : Springer International Publishing AG,c2024 9783031493706 320 $aIncludes bibliographical references and index. 327 $aGeneral 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. 330 $aThis monograph presents the most recent developments in the study of Hamilton-Jacobi equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text. After an initial section that provides a ?toolbox? containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text ? such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization ? and several key open problems are presented. This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi equations, network problems, or scalar conservation laws. 410 0$aPNLDE Subseries in Control,$x2731-7374 ;$v104 606 $aDifferential equations 606 $aMathematical optimization 606 $aCalculus of variations 606 $aSystem theory 606 $aControl theory 606 $aDifferential Equations 606 $aCalculus of Variations and Optimization 606 $aSystems Theory, Control 606 $aEquacions de Hamilton-Jacobi$2thub 606 $aEquacions en derivades parcials$2thub 608 $aLlibres electrònics$2thub 615 0$aDifferential equations. 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aSystem theory. 615 0$aControl theory. 615 14$aDifferential Equations. 615 24$aCalculus of Variations and Optimization. 615 24$aSystems Theory, Control. 615 7$aEquacions de Hamilton-Jacobi 615 7$aEquacions en derivades parcials 676 $a515.353 700 $aBarles$b Guy$062880 702 $aChasseigne$b Emmanuel 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910799203803321 996 $aOn Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities$93872866 997 $aUNINA