{"product_id":"9783030110987","title":"Progress in Nonlinear Differential Equations and Their Applications","description":"\u003ch1\u003eProgress in Nonlinear Differential Equations and Their Applications\u003c\/h1\u003e \u003ch2\u003eMunteanu, Ionuţ\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThis monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThe text provides answers to the following problems, which are of great practical importance:\u003c\/div\u003e\u003cdiv\u003e\u003cul\u003e\n\u003cli\u003eDesigning the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eDesigning observers for the considered control systems\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eConstructing time-discrete controllers requiring only partial knowledge of the state\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/div\u003e\u003cdiv\u003eAfter reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more.\u003cbr\u003e\n\u003c\/div\u003e\u003cdiv\u003e \u003c\/div\u003e\u003cdiv\u003e\n\u003ci\u003eBoundary Stabilization of Parabolic Equations\u003c\/i\u003e will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-03-01\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030110987\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-11099-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 214\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45378504097932,"sku":"9783030110987","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030110987_9ddbf448-c9df-45af-af42-204b7a88567a.jpg?v=1775703891","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030110987","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}