LEADER 03230nam 2200553 450 001 9910495248303321 005 20230427102236.0 010 $a981-16-2663-4 024 7 $a10.1007/978-981-16-2663-0 035 $a(CKB)4100000011996789 035 $a(DE-He213)978-981-16-2663-0 035 $a(MiAaPQ)EBC6698938 035 $a(Au-PeEL)EBL6698938 035 $a(PPN)257352309 035 $a(EXLCZ)994100000011996789 100 $a20220427d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAbstract parabolic evolution equations and Lojasiewicz-Simon inequality$hII$iApplications /$fAtsushi Yagi 205 $a1st ed. 2021. 210 $d??2021. 210 1$aGateway East, Singapore :$cSpringer,$d[2021] 215 $a1 online resource (IX, 128 p. 607 illus.) 225 1 $aSpringerBriefs in mathematics 311 $a981-16-2662-6 327 $aPreliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model. 330 $aThis second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the ?ojasiewicz?Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller?Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed. 410 0$aSpringerBriefs in mathematics. 606 $aAnàlisi matemàtica$2thub 606 $aAnàlisi funcional$2thub 606 $aTeoria de la mesura$2thub 606 $aEvolution equations 608 $aLlibres electrònics$2thub 615 7$aAnàlisi matemàtica 615 7$aAnàlisi funcional 615 7$aTeoria de la mesura 615 0$aEvolution equations. 676 $a515.353 700 $aYagi$b Atsushi$f1951-$01075921 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910495248303321 996 $aAbstract parabolic evolution equations and Lojasiewicz-Simon inequality$92835434 997 $aUNINA