Author | Pazy, A. author |
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Title | Semigroups of Linear Operators and Applications to Partial Differential Equations [electronic resource] / by A. Pazy |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5561-1 |
Descript | X, 282 p. online resource |
1 Generation and Representation -- 1.1 Uniformly Continuous Semigroups of Bounded Linear Operators -- 1.2 Strongly Continuous Semigroups of Bounded Linear Operators -- 1.3 The Hille-Yosida Theorem -- 1.4 The Lumer Phillips Theorem -- 1.5 The Characterization of the Infinitesimal Generators of C0 Semigroups -- 1.6 Groups of Bounded Operators -- 1.7 The Inversion of the Laplace Transform -- 1.8 Two Exponential Formulas -- 1.9 Pseudo Resolvents -- 1.10 The Dual Semigroup -- 2 Spectral Properties and Regularity -- 2.1 Weak Equals Strong -- 2.2 Spectral Mapping Theorems -- 2.3 Semigroups of Compact Operators -- 2.4 Differentiability -- 2.5 Analytic Semigroups -- 2.6 Fractional Powers of Closed Operators -- 3 Perturbations and Approximations -- 3.1 Perturbations by Bounded Linear Operators -- 3.2 Perturbations of Infinitesimal Generators of Analytic Semigroups -- 3.3 Perturbations of Infinitesimal Generators of Contraction Semigroups -- 3.4 The Trotter Approximation Theorem -- 3.5 A General Representation Theorem -- 3.6 Approximation by Discrete Semigroups -- 4 The Abstract Cauchy Problem -- 4.1 The Homogeneous Initial Value Problem -- 4.2 The Inhomogeneous Initial Value Problem -- 4.3 Regularity of Mild Solutions for Analytic Semigroups -- 4.4 Asymptotic Behavior of Solutions -- 4.5 Invariant and Admissible Subspaces -- 5 Evolution Equations -- 5.1 Evolution Systems -- 5.2 Stable Families of Generators -- 5.3 An Evolution System in the Hyperbolic Case -- 5.4 Regular Solutions in the Hyperbolic Case -- 5.5 The Inhomogeneous Equation in the Hyperbolic Case -- 5.6 An Evolution System for the Parabolic Initial Value Problem -- 5.7 The Inhomogeneous Equation in the Parabolic Case -- 5.8 Asymptotic Behavior of Solutions in the Parabolic Case -- 6 Some Nonlinear Evolution Equations -- 6.1 Lipschitz Perturbations of Linear Evolution Equations -- 6.2 Semilinear Equations with Compact Semigroups -- 6.3 Semilinear Equations with Analytic Semigroups -- 6.4 A Quasilinear Equation of Evolution -- 7 Applications to Partial Differential EquationsโLinear Equations -- 7.1 Introduction -- 7.2 Parabolic EquationsโL2 Theory -- 7.3 Parabolic EquationsโLp Theory -- 7.4 The Wave Equation -- 7.5 A Schrรถdinger Equation -- 7.6 A Parabolic Evolution Equation -- 8 Applications to Partial Differential EquationsโNonlinear Equations -- 8.1 A Nonlinear Schrรถinger Equation -- 8.2 A Nonlinear Heat Equation in R1 -- 8.3 A Semilinear Evolution Equation in R3 -- 8.4 A General Class of Semilinear Initial Value Problems -- 8.5 The Korteweg-de Vries Equation -- Bibliographical Notes and Remarks