{"product_id":"attractors-for-infinite-dimensional-non-autonomous-dynamical-systems-hardcover","title":"Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems - Hardcover","description":"\u003cp\u003eby \u003cb\u003eAlexandre Carvalho\u003c\/b\u003e (Author), \u003cb\u003eJosé a. Langa\u003c\/b\u003e (Author), \u003cb\u003eJames Robinson\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. \u003c\/p\u003e \u003cp\u003eThe book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional examples.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe purpose of the book is to provide a summary of the current theory, starting with basic definitions and proceeding all the way to state-of-the-art results. As such it is intended as a primer for graduate students, and a reference for more established researchers in the field.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe basic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finite-dimensional, and structural results for pullback attractors for small non-autonomous perturbations of gradient systems (those with a Lyapunov function). The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows in particular that such systems are stable under perturbation.\u003c\/p\u003e\u003cp\u003eApplication of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: a self-contained development of these topics is given in full.\u003c\/p\u003e\u003cp\u003eAfter providing all the necessary theory the book treats a number of model problems in detail, demonstrating the wide applicability of the definitions and techniques introduced: these include a simple Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equations, general reaction-diffusion problems, a non-autonomous version of the Chafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous damped wave equation.\u003c\/p\u003e \u003cp\u003eAlexandre N. Carvalho is a Professor at the University of Sao Paulo, Brazil. José A. Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eAlexandre N. Carvalho is a Professor at University of Sao Paulo, Brazil. José A. Langa is a Professor at University of Seville, Spain. James C. Robinson is a Professor at University of Warwick, UK.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 412\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 26, 2012\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":47434693148850,"sku":"9781461445807","price":178.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0770\/3891\/1666\/files\/2bd12ae4d22f9916c4b210ac27edfee1.webp?v=1778620017","url":"https:\/\/box.dadyminds.org\/products\/attractors-for-infinite-dimensional-non-autonomous-dynamical-systems-hardcover","provider":"DADYMINDS BOX","version":"1.0","type":"link"}