{"product_id":"semiconcave-functions-hamilton-jacobi-equations-and-optimal-control","title":"Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control","description":"\u003cp\u003eIn this review of Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control the reviewer finds a rigorous, self-contained treatment aimed at graduate students and researchers who need a deep theoretical foundation. The book's single biggest reason to buy is its comprehensive exposition of \u003cstrong\u003esemiconcavity theory\u003c\/strong\u003e and its clear linkage to both optimal control and viscosity solutions, making it a unique reference for those developing or applying analytical methods to Hamilton-Jacobi problems.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive theory:\u003c\/strong\u003e The book presents the general theory of semiconcave functions with full proofs, so readers gain a complete understanding rather than a collection of isolated results.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eApplications-focused:\u003c\/strong\u003e Later chapters apply the theory to the Bolza problem and optimal exit time problems, illustrating how abstract results inform concrete control problems.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSelf-contained prerequisites:\u003c\/strong\u003e Included material from convex analysis, nonsmooth analysis, and viscosity solutions reduces the need for additional textbooks when approaching the text.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eIllustrative examples:\u003c\/strong\u003e Significant examples accompany theory to clarify subtle points and demonstrate typical behaviors encountered in applied problems.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSuitable for research:\u003c\/strong\u003e The level and scope make it a practical reference for mathematicians working on nonlinear differential equations and control theory.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThe primary audience is graduate students in applied mathematics and researchers in optimal control, partial differential equations, or calculus of variations who require a rigorous source on \u003cstrong\u003esemiconcave functions\u003c\/strong\u003e. It also suits teachers preparing advanced courses on Hamilton-Jacobi equations who want a single-volume reference for both theory and applications.\u003c\/p\u003e\n\u003cp\u003ePractitioners seeking quick computational recipes or an elementary introduction should look elsewhere, since the book emphasizes rigorous development and proofs rather than algorithmic implementation or introductory exposition.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThorough presentation of semiconcavity that consolidates scattered literature into a unified account.\u003c\/li\u003e\n\u003cli\u003eClear treatment of applications to the Bolza problem and optimal exit time, linking theory to classical control problems.\u003c\/li\u003e\n\u003cli\u003eSelf-contained appendices on convex and nonsmooth analysis reduce external prerequisites for motivated readers.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe text is demanding and assumes mathematical maturity, so it is not a casual or introductory read for non-specialists.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eSemiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eProgress in Nonlinear Differential Equations and Their Applications, 58\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003ePiermarco Cannarsa, Carlo Sinistrari\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eCoverage\u003c\/td\u003e\n\u003ctd\u003eTheory of semiconcave functions and applications to optimal control\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApplications\u003c\/td\u003e\n\u003ctd\u003eBolza problem; optimal exit time problems for nonlinear control systems\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncludes\u003c\/td\u003e\n\u003ctd\u003ePrerequisites from convex analysis, nonsmooth analysis, and viscosity solutions\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eFor serious students and researchers in differential equations and control theory this book is an authoritative, good-value reference that ties abstract \u003cstrong\u003esemiconcavity\u003c\/strong\u003e to concrete optimal control problems. Its self-contained style and breadth make it a durable addition to an academic library, though casual readers should expect a steep learning curve.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes the book require prior knowledge of convex analysis?\u003c\/strong\u003e\u003cbr\u003eThe book includes the necessary material on convex analysis and nonsmooth analysis, so it is largely self-contained for readers with sufficient mathematical maturity.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAre practical control algorithms covered?\u003c\/strong\u003e\u003cbr\u003eThe focus is theoretical: applications to control problems are analytical rather than algorithmic, so readers looking for numerical methods should consult complementary sources.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs this suitable for a semester course?\u003c\/strong\u003e\u003cbr\u003eYes, motivated instructors can base an advanced graduate course on this text, especially for topics connecting Hamilton-Jacobi equations and optimal control.\u003c\/p\u003e","brand":"Piermarco Cannarsa, Carlo Sinstrari","offers":[{"title":"Default Title","offer_id":48779892916443,"sku":"0817643362","price":89.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61hTzlpzegL._SL1233.jpg?v=1778964519","url":"https:\/\/gearmusthave.com\/products\/semiconcave-functions-hamilton-jacobi-equations-and-optimal-control","provider":"GearMustHave","version":"1.0","type":"link"}