C₀-semigroups and applications. (2003)

• Record Type: Book
• Further Information: Note: Ioan I. Vrabie.
• Other Names: Vrabie, I. I (Ioan I.), 1951-
• Contents: Cover -- Contents -- Preface -- Chapter 1. Preliminaries -- 1.1. Vector-Valued Measurable Functions -- 1.2. The Bochner Integral -- 1.3. Basic Function Spaces -- 1.4. Functions of Bounded Variation -- 1.5. Sobolev Spaces -- 1.6. Unbounded Linear Operators -- 1.7. Elements of Spectral Analysis -- 1.8. Functional Calculus for Bounded Operators -- 1.9. Functional Calculus for Unbounded Operators -- Problems -- Notes -- Chapter 2. Semigroups of Linear Operators -- 2.1. Uniformly Continuous Semigroups -- 2.2. Generators of Uniformly Continuous Semigroups -- 2.3. C0-Semigroups. General Properties -- 2.4. The Infinitesimal Generator -- Problems -- Notes -- Chapter 3. Generation Theorems -- 3.1. The Hille-Yosida Theorem. Necessity -- 3.2. The Hille-Yosida Theorem. Sufficiency -- 3.3. The Feller-Miyadera-Phillips Theorem -- 3.4. The Lumer-Phillips Theorem -- 3.5. Some Consequences -- 3.6. Examples -- 3.7. The Dual of a C0-Semigroup -- 3.8. The Sun Dual of a C0-Semigroup -- 3.9. Stone Theorem -- Problems -- Notes -- Chapter 4. Differential Operators Generating C0- Semigroups -- 4.1. The Laplace Operator with Dirichlet Boundary Condition -- 4.2. The Laplace Operator with Neumann Boundary Condition -- 4.3. The Maxwell Operator -- 4.4. The Directional Derivative -- 4.5. The Schrödinger Operator -- 4.6. The Wave Operator -- 4.7. The Airy Operator -- 4.8. The Equations of Linear Thermoelasticity -- 4.9. The Equations of Linear Viscoelasticity -- Problems -- Notes -- Chapter 5. Approximation Problems and Applications -- 5.1. The Continuity of A?etA -- 5.2. The Chernoff and Lie-Trotter Formulae -- 5.3. A Perturbation Result -- 5.4. The Central Limit Theorem -- 5.5. Feynman Formula -- 5.6. The Mean Ergodic Theorem -- Problems -- Notes -- Chapter 6. Some Special Classes of C0-Semigroups -- 6.1. Equicontinuous Semigroups -- 6.2. Compact Semigroups -- 6.3. Differentiable Semigroups -- 6.4. Semigroups with Symmetric Generators -- 6.5. The Linear Delay Equation -- Problems -- Notes -- Chapter 7. Analytic Semigroups -- 7.1. Definition and Characterizations -- 7.2. The Heat Equation -- 7.3. The Stokes Equation -- 7.4. A Parabolic Problem with Dynamic Boundary Conditions -- 7.5. An Elliptic Problem with Dynamic Boundary Conditions -- 7.6. Fractional Powers of Closed Operators -- 7.7. Further Investigations in the Analytic Case -- Problems -- Notes -- Chapter 8. The Nonhomogeneous Cauchy Problem -- 8.1. The Cauchy Problem u' = Au + f, u(a) =? -- 8.2. Smoothing Effect. The Hilbert Space Case -- 8.3. An Approximation Result -- 8.4. Compactness of the Solution Operator from LP(a, b ; X -- 8.5. The Case when (?I -- A) -1 is Compact -- 8.6. Compactness of the Sol.
• Publisher Details: Place of publication not identified : JAI Press
• Publication Date: 2003
• Extent: 1 online resource (396 pages)
• Subjects: 515/.724; Semigroups of operators; Semigroups of operators; Halbgruppe; Halbgruppe
• Languages: English
• ISBNs: 9780080530048; 0080530044
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.