LEADER 05775nam 22008055 450 001 9910438137303321 005 20200703160032.0 010 $a1-4614-4581-7 024 7 $a10.1007/978-1-4614-4581-4 035 $a(CKB)2670000000530199 035 $a(EBL)1156151 035 $a(OCoLC)831115935 035 $a(SSID)ssj0000766939 035 $a(PQKBManifestationID)11442118 035 $a(PQKBTitleCode)TC0000766939 035 $a(PQKBWorkID)10739155 035 $a(PQKB)10702138 035 $a(DE-He213)978-1-4614-4581-4 035 $a(MiAaPQ)EBC1156151 035 $a(PPN)168300672 035 $a(EXLCZ)992670000000530199 100 $a20120928d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAttractors for infinite-dimensional non-autonomous dynamical systems /$fby Alexandre Carvalho, José A. Langa, James Robinson 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (433 p.) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v182 300 $aDescription based upon print version of record. 311 $a1-4614-4580-9 311 $a1-4899-9176-X 320 $aIncludes bibliographical references and index. 327 $aThe pullback attractor -- Existence results for pullback attractors -- Continuity of attractors -- Finite-dimensional attractors -- Gradient semigroups and their dynamical properties -- Semilinear Differential Equations -- Exponential dichotomies -- Hyperbolic solutions and their stable and unstable manifolds -- A non-autonomous competitive Lotka-Volterra system -- Delay differential equations.-The Navier?Stokes equations with non-autonomous forcing.-  Applications to parabolic problems -- A non-autonomous Chafee?Infante equation -- Perturbation of diffusion and continuity of attractors with rate -- A non-autonomous damped wave equation -- References -- Index.-. 330 $aThis book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional examples.   The purpose of the book is to provide a summary of the current theory, starting with basic definitions and proceeding all the way to state-of-the-art results. As such it is intended as a primer for graduate students, and a reference for more established researchers in the field.   The basic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finite-dimensional, and structural results for pullback attractors for small non-autonomous perturbations of gradient systems (those with a Lyapunov function).  The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows in particular that such systems are stable under perturbation. Application of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: a self-contained development of  these topics is given in full. After providing all the necessary theory the book treats a number of model problems in detail, demonstrating the wide applicability of the definitions and techniques introduced: these include a simple Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equations, general reaction-diffusion problems, a non-autonomous version of the Chafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous damped wave equation. Alexandre N. Carvalho is a Professor at the University of Sao Paulo, Brazil. José A. Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v182 606 $aPartial differential equations 606 $aDynamics 606 $aErgodic theory 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 610 4$aMathematics. 610 4$aDifferentiable dynamical systems. 610 4$aDifferential equations, partial. 610 4$aCell aggregation -- Mathematics. 610 4$aPartial Differential Equations. 610 4$aDynamical Systems and Ergodic Theory. 610 4$aManifolds and Cell Complexes (incl. Diff. Topology) 615 0$aPartial differential equations. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 14$aPartial Differential Equations. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 676 $a514.74 700 $aCarvalho$b Alexandre$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064944 702 $aLanga$b José A$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRobinson$b James$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910438137303321 996 $aAttractors for infinite-dimensional non-autonomous dynamical systems$92541874 997 $aUNINA