05173nam 22006614a 450 991078507140332120200520144314.0981-277-729-6(CKB)1000000000411626(EBL)1679507(OCoLC)879023495(SSID)ssj0000151399(PQKBManifestationID)11151316(PQKBTitleCode)TC0000151399(PQKBWorkID)10319936(PQKB)11418063(MiAaPQ)EBC1679507(WSP)00004990(Au-PeEL)EBL1679507(CaPaEBR)ebr10201327(CaONFJC)MIL505401(PPN)181361175(EXLCZ)99100000000041162620020528d2002 uy 0engur|n|---|||||txtccrEvolution equations and approximations[electronic resource] /Kazufumi Ito, Franz KappelRiver Edge, N.J. World Scientificc20021 online resource (518 p.)Series on advances in mathematics for applied sciences ;v. 61Description based upon print version of record.981-238-026-4 Includes bibliographical references (p. 489-492) and index.Contents ; 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 operators1.5 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 equationChapter 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 theorem4.4 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 diffusionChapter 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 solutions6.6 Autonomous problems 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 Series on advances in mathematics for applied sciences ;v. 61.Evolution equationsNumerical solutionsApproximation theoryEvolution equationsNumerical solutions.Approximation theory.515/.353Ito Kazufumi311866Kappel F13975MiAaPQMiAaPQMiAaPQBOOK9910785071403321Evolution equations and approximations1419468UNINA