Evolution equations and approximations [[electronic resource] /] / Kazufumi Ito, Franz Kappel

• Autore: Ito Kazufumi
• Pubblicazione: River Edge, N.J., : World Scientific, c2002
• Descrizione fisica: 1 online resource (518 p.)
• Disciplina: 515/.353
• Soggetto topico: Evolution equations - Numerical solutions; Approximation theory
• Soggetto genere / forma: Electronic books.
• Altri autori: KappelF
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 489-492) and index.
• Nota di contenuto: 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 operators ; 1.5 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 ; Chapter 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 ; 4.4 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 ; Chapter 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 ; 6.6 Autonomous problems
• Sommario/riassunto: 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
• Titolo autorizzato: Evolution equations and approximations
• ISBN: 981-277-729-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910450915003321
• Lo trovi qui: Univ. Federico II
• Serie: Series on advances in mathematics for applied sciences ; ; v. 61.