| Description |
1 online resource (372 pages) |
| Series |
Chapman and Hall/CRC Monographs and Research Notes in Mathematics Ser |
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Chapman and Hall/CRC Monographs and Research Notes in Mathematics Ser
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| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; About the Authors; Symbol Description; 1: Basic Concepts; 1.1 Introduction; 1.2 Chapter Summaries; 2: Coagulation and Fragmentation; 2.1 Coagulation and Fragmentation Processes; 2.2 Coagulation and Fragmentation Equations; 2.2.1 Discrete Size Equations; 2.2.2 Continuous Size Equations; 2.2.3 Coagulation and Fragmentation Rate Coefficients; 2.2.3.1 Coagulation Coefficients; 2.2.3.2 Fragmentation Coefficients; 2.3 Review of Previous Mathematical Investigations |
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2.3.1 Moments, Mass Conservation, Gelation and Shattering2.3.2 Closed-Form Solutions; 2.3.2.1 The Fragmentation Equation; 2.3.2.2 The Coagulation Equation; 2.3.2.3 The Coagulation-Fragmentation Equation; 2.3.3 Detailed Balance Condition and Stationary Solutions; 2.3.4 Self-Similar Solutions; 2.3.5 Existence and Uniqueness Results; 2.3.6 Asymptotic Behaviour of Solutions; 2.4 Equations Incorporating Other Factors; 2.4.1 Growth or Decay Terms; 2.4.2 Time-Dependent Rate Coefficients; 2.4.3 Coagulation-Fragmentation with Spatial Interactions; 2.4.4 Equations with Several State Variables |
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2.4.5 Nonlinear Fragmentation3: Mathematical Toolbox I; 3.1 Basic Functional Analytic Results; 3.1.1 Function Spaces; 3.1.2 Spaces of Vector-valued Functions and Spaces of Type L; 3.1.3 Operators; 3.1.4 Banach Spaces of Coagulation-Fragmentation Theory; 3.2 Order in Banach Spaces; 3.2.1 Basic Notions and Definitions; 3.2.2 Positive Operators; 3.2.3 Order and Norm; 3.2.4 Sublattices and Ideals; 3.2.4.1 Irreducible Operators; 3.2.5 Complexification; 4: Semigroup Methods for Fragmentation Models; 4.1 Why Do We Need Semigroups to Study Fragmentation Problems? |
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4.1.1 Breach of Mass Conservation Principle4.1.2 Multiple Solutions; 4.1.3 Operator Realisations of Differential and Integral Expressions in Evolution Equations; 4.2 Generation Theorems; 4.2.1 Basic Properties of Semigroups; 4.2.2 Spectrum of an Operator; 4.2.3 Hille-Yosida Theorem; 4.2.4 Dissipative Operators; 4.2.5 Analytic Semigroups; 4.3 Uniqueness and Non-uniqueness of Solutions of Evolution Equations; 4.4 Fractional Powers, Interpolation and Extrapolation Spaces; 4.4.1 Fractional Powers of Generators; 4.4.2 Interpolation Spaces; 4.4.3 Extrapolation Spaces; 4.5 Positive Semigroups |
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4.5.1 Generation Results for Positive Semigroups4.5.1.1 Lumer-Phillips Theorem for Positive Contractions; 4.5.1.2 Arendt-Batty-Robinson Theorem; 4.6 Spectral Properties and Long-Term Behaviour of Semigroups; 4.6.1 Spectral Mapping Theorem; 4.6.2 Essential Growth Bound; 4.6.3 Peripheral Spectrum of Positive Semigroups; 4.7 Inhomogeneous Problems; 4.8 Semilinear Problems; 4.9 Perturbation Methods; 4.9.1 A Spectral Criterion; 4.9.2 Bounded Perturbation Theorem; 4.9.3 Miyadera Perturbation; 4.9.4 Perturbation of Resolvent Positive Operators; 4.9.5 Kato-Voigt Perturbation Results |
| Notes |
4.9.6 Arendt-Rhandi Theorem on Positive Analytic Semigroups |
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Print version record |
| Form |
Electronic book
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| Author |
Lamb, Wilson
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Laurencot, Philippe
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| ISBN |
9781351650465 |
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1351650467 |
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