LEADER 05173nam 22006614a 450 001 9910785071403321 005 20200520144314.0 010 $a981-277-729-6 035 $a(CKB)1000000000411626 035 $a(EBL)1679507 035 $a(OCoLC)879023495 035 $a(SSID)ssj0000151399 035 $a(PQKBManifestationID)11151316 035 $a(PQKBTitleCode)TC0000151399 035 $a(PQKBWorkID)10319936 035 $a(PQKB)11418063 035 $a(MiAaPQ)EBC1679507 035 $a(WSP)00004990 035 $a(Au-PeEL)EBL1679507 035 $a(CaPaEBR)ebr10201327 035 $a(CaONFJC)MIL505401 035 $a(PPN)181361175 035 $a(EXLCZ)991000000000411626 100 $a20020528d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEvolution equations and approximations$b[electronic resource] /$fKazufumi Ito, Franz Kappel 210 $aRiver Edge, N.J. $cWorld Scientific$dc2002 215 $a1 online resource (518 p.) 225 1 $aSeries on advances in mathematics for applied sciences ;$vv. 61 300 $aDescription based upon print version of record. 311 $a981-238-026-4 320 $aIncludes bibliographical references (p. 489-492) and index. 327 $aContents ; Preface ; Chapter 1. Dissipative and Maximal Monotone Operators ; 1.1 Duality mapping and directional derivatives of norms ; 1.2 Dissipative operators ; 1.3 Properties of m-dissipative operators ; 1.4 Perturbation results for m-dissipative operators 327 $a1.5 Maximal monotone operators 1.6 Convex functionals and subdifferentials ; Chapter 2. Linear Semigroups ; 2.1 Examples and basic definitions ; 2.2 Cauchy problems and mild solutions ; 2.3 The Hille-Yosida theorem ; 2.4 The Lumer-Phillips theorem ; 2.5 A second order equation 327 $aChapter 3. Analytic Semigroups 3.1 Dissipative operators and sesquilinear forms ; 3.2 Analytic semigroups ; Chapter 4. Approximation of Co-Semigroups ; 4.1 The Trotter-Kato theorem ; 4.2 Approximation of nonhomogeneous problems ; 4.3 Variational formulations of the Trotter-Kato theorem 327 $a4.4 An approximation result for analytic semigroups Chapter 5. Nonlinear Semigroups of Contractions ; 5.1 Generation of nonlinear semigroups ; 5.2 Cauchy problems with dissipative operators ; 5.3 The infinitesimal generator ; 5.4 Nonlinear diffusion 327 $aChapter 6. Locally Quasi-Dissipative Evolution Equations 6.1 Locally quasi-dissipative operators ; 6.2 Assumptions on the operators A(t) ; 6.3 DS-approximations and fundamental estimates ; 6.4 Existence of DS-approximations ; 6.5 Existence and uniqueness of mild solutions 327 $a6.6 Autonomous problems 330 $a This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems. The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and 410 0$aSeries on advances in mathematics for applied sciences ;$vv. 61. 606 $aEvolution equations$xNumerical solutions 606 $aApproximation theory 615 0$aEvolution equations$xNumerical solutions. 615 0$aApproximation theory. 676 $a515/.353 700 $aIto$b Kazufumi$0311866 701 $aKappel$b F$013975 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910785071403321 996 $aEvolution equations and approximations$91419468 997 $aUNINA