{"product_id":"controllability-and-stabilization-of-parabolic-equations-advanced","title":"Controllability and Stabilization of Parabolic Equations - Advanced","description":"\u003cp\u003eIn this review of Controllability and Stabilization of Parabolic Equations the focus is on advanced methods for researchers and graduate students in control theory and applied PDEs. The monograph delivers a rigorous, methodical treatment of \u003cstrong\u003econtrollability techniques\u003c\/strong\u003e for parabolic boundary value problems and shows why it is valuable for those needing tools to represent and control diffusion-like systems. The single biggest reason to buy is its detailed combination of Carleman inequalities, spectral decomposition, and practical stabilization strategies that connect theory to boundary control problems.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eCarleman inequality foundation:\u003c\/strong\u003e Presents the fundamental Carleman estimates used to obtain observability and controllability results for linear parabolic equations, giving readers the theoretical backbone for further study.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSpectral decomposition technique:\u003c\/strong\u003e Explains how spectral methods represent parabolic solutions, which helps in both analysis and numerical approximation of heat and diffusion systems.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eWide class applicability:\u003c\/strong\u003e Develops approaches designed to cover a broad class of parabolic systems, so readers can adapt methods to heat, diffusion, and related equations.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFinite-mode stabilization:\u003c\/strong\u003e Details a stabilizing feedback controller approach that uses a finite number of unstable modes, making stabilization tractable in many practical settings.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eBoundary stabilization for fluid models:\u003c\/strong\u003e Applies the developed methods to the Navier-Stokes boundary stabilization problem, showing how the techniques extend to viscous fluid motion.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is aimed at advanced graduate students, researchers, and practitioners in control theory, applied mathematics, and engineering who need a rigorous reference on controllability and stabilization for parabolic PDEs. It is especially useful for those working on theoretical aspects of boundary control, spectral methods, or stabilization of diffusion and fluid systems.\u003c\/p\u003e\n\u003cp\u003eThose looking for an introductory text or a computational how-to manual with step-by-step code examples should look elsewhere, because the monograph emphasizes mathematical proofs and theoretical development over software implementation or elementary 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 theoretical development of \u003cstrong\u003eCarleman inequalities\u003c\/strong\u003e that underpin controllability results.\u003c\/li\u003e\n\u003cli\u003eClear presentation of the \u003cstrong\u003espectral decomposition\u003c\/strong\u003e technique useful for representing parabolic solutions.\u003c\/li\u003e\n\u003cli\u003ePractical stabilization strategy using a finite number of modes, bridging theory and applied boundary control.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eFocus is heavily theoretical, so readers seeking applied computational recipes or extensive numerical examples may find it limited.\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\u003eControllability and Stabilization of Parabolic Equations\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003ePNLDE Subseries in Control\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eViorel Barbu\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMain topics\u003c\/td\u003e\n\u003ctd\u003eCarleman inequalities, controllability, stabilization, spectral decomposition\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApplications discussed\u003c\/td\u003e\n\u003ctd\u003eHeat and diffusion equations, boundary stabilization of Navier-Stokes\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApproach\u003c\/td\u003e\n\u003ctd\u003eTheoretical proofs with applied-method connections\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eControllability and Stabilization of Parabolic Equations is a strong value for readers who need a rigorous, mathematically precise treatment of control methods for parabolic PDEs. It is best for researchers and advanced students who will benefit from its combination of Carleman-based analysis, spectral representation, and finite-mode stabilization techniques applied to diffusion and fluid boundary control.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book cover numerical methods?\u003c\/strong\u003e\u003cbr\u003eThe focus is theoretical; numerical implementation details are limited and the book does not provide extensive code examples.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs prior knowledge required?\u003c\/strong\u003e\u003cbr\u003eYes. A solid background in PDEs, functional analysis, and control theory is recommended to follow the proofs and methods.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAre Navier-Stokes applications included?\u003c\/strong\u003e\u003cbr\u003eYes. The book discusses boundary stabilization approaches applied to Navier-Stokes equations for viscous fluid motion.\u003c\/p\u003e","brand":"Viorel Barbu","offers":[{"title":"Default Title","offer_id":48609416970459,"sku":"3030095509","price":89.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61hhh-E2l-L._SL1254.jpg?v=1778502694","url":"https:\/\/gearmusthave.com\/products\/controllability-and-stabilization-of-parabolic-equations-advanced","provider":"GearMustHave","version":"1.0","type":"link"}