LEADER 04720nam 22007935 450 001 9910300241703321 005 20221020225821.0 010 $a3-319-23407-2 024 7 $a10.1007/978-3-319-23407-6 035 $a(CKB)3710000000474126 035 $a(EBL)4178537 035 $a(SSID)ssj0001584994 035 $a(PQKBManifestationID)16265404 035 $a(PQKBTitleCode)TC0001584994 035 $a(PQKBWorkID)14865777 035 $a(PQKB)10105402 035 $a(DE-He213)978-3-319-23407-6 035 $a(MiAaPQ)EBC4178537 035 $a(PPN)190523441 035 $a(EXLCZ)993710000000474126 100 $a20150905d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe convergence problem for dissipative autonomous systems $eclassical methods and recent advances /$fby Alain Haraux, Mohamed Ali Jendoubi 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (147 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-23406-4 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a1 Introduction -- 2 Some basic tools -- 3 Background results on Evolution Equations.- 4 Uniformly damped linear semi-groups.- 5 Generalities on dynamical systems.- 6 The linearization method.- 7 Gradient-like systems.- 8 Liapunov?s second method - invariance principle.- 9 Some basic examples.- 10 The convergence problem in finite dimensions -- 11 The infinite dimensional case -- 12 Variants and additional results. 330 $aThe book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywhere in a readily applicable form. The applications covered in this short text are the simplest, but more complicated cases are mentioned in the final chapter, together with references to the corresponding specialized papers. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations, Partial 606 $aFunctional analysis 606 $aOperator theory 606 $aDifferential equations 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations, Partial. 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aDifferential equations. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aPartial Differential Equations. 615 24$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aOrdinary Differential Equations. 676 $a515.24 700 $aHaraux$b Alain$4aut$4http://id.loc.gov/vocabulary/relators/aut$042671 702 $aJendoubi$b Mohamed Ali$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300241703321 996 $aThe Convergence Problem for Dissipative Autonomous Systems$92533256 997 $aUNINA