Analytic methods for coagulation-fragmentation models / Jacek Banasiak, Wilson Lamb, Philippe Laurençot.

Format:

Book

Author/Creator:

Banasiak, J., author.

Lamb, Wilson, author.

Laurençot, Philippe, author.

Series:

Monographs and research notes in mathematics

Language:

English

Subjects (All):

Coagulation.

Aggregation (Chemistry).

Semigroups.

Fragmentation reactions.

Physical Description:

2 volumes (xviii, 675 pages) ; 26 cm.

Other Title:

Analytic methods for coagulation fragmentation models

Place of Publication:

Boca Raton, FL : CRC Press, Taylor & Francis Group, [2020]

Contents:

Machine generated contents note: 6. Introduction to Volume II

6.1. Introduction

6.2. Chapter Summaries

7. Mathematical Toolbox II

7.1. Weak Topology and Related Results

7.2. Continuous and Compact Embeddings

7.3. Dynamical Systems

7.3.1. Basic Concepts

7.3.2. Stationary Solutions and Fixed-Point Theorems

7.4. Algebraic Inequalities

7.5. The Gronwall

Henry Inequality

8. Solvability of Coagulation-Fragmentation Equations

8.1. Coagulation-Fragmentation Equations via Semigroups

8.1.1. Global Classical Solutions of Transport-Coagulation-Fragmentation Equations with Bounded Coagulation Kernels

8.1.2. Global Classical Solutions of Coagulation-Fragmentation Equations with Unbounded Coagulation Kernels

8.2. Coagulation-Fragmentation Equations via Weak Compactness

8.2.1. Truncated Kernels and Basic Estimates

8.2.1.1. Truncated Kernels

8.2.1.2. Weak Stability

8.2.1.3. Lower Bounds for Coagulation

8.2.1.4. Upper Bounds for Coagulation: Moment Estimates

8.2.1.5. Upper Bounds for Coagulation: Lp-estimates

8.2.1.6. Positivity

8.2.2. Mass-Conserving Solutions

8.2.2.1. Coagulation Kernel with Linear Growth

8.2.2.2. Coagulation Kernel with Linear Growth and Integrable Daughter Distribution Function b

8.2.2.3. Coagulation Kernel with Linear Growth and Non-integrable Daughter Distribution Function b

8.2.2.4. Strong Fragmentation

8.2.3. Weak Solutions

8.2.4. Singular Coagulation Coefficients

8.2.5. Uniqueness

9. Gelation and Shattering

9.1. Gelation

9.2. Instantaneous Gelation

9.3. Shattering

10. Long-Term Behaviour

10.1. Continuous Fragmentation

10.1.1. Self-Similar Profiles

10.1.2. Convergence and Decay Rates

10.1.2.1. Convergence

10.1.2.2. Decay Rates

10.2. Coagulation

10.2.1. The Constant Coagulation Kernel k(x, y) = 2

10.2.2. The Additive Coagulation Kernel k+(x, y) = x + y

10.2.3. The Diagonal Coagulation Kernel k(x, y) = r(x)δx-y

10.2.4. Mass-Conserving Self-Similar Profiles

10.2.4.1. A Discrete Approximation Scheme

10.2.4.2. Moment Estimates

10.2.4.3. Integrability Estimates

10.2.4.4. Existence of Mass-Conserving Self-Similar Profiles

10.2.5. Regularity of Mass-Conserving Self-Similar Profiles

10.2.6. Other Self-Similar Profiles

10.2.6.1. Self-Similar Profiles: λ = 1

10.2.6.2. Self-Similar Profiles with Infinite Mass

10.3. Coagulation-Fragmentation

10.3.1. The Aizenman

Bak Result for Constant Coefficients

10.3.2. Detailed Balance

10.3.2.1. Existence

10.3.2.2. Entropy Identity

10.3.2.3. Stabilisation

10.3.2.4. Convergence

10.3.3. Stationary Solutions

10.3.3.1. Additive Coagulation and Constant Fragmentation

10.3.3.2. Singular Coagulation and Strong Fragmentation

10.3.3.3. Other Stationary Solutions

10.3.4. Mass-Conserving Self-Similar Solutions

11. Miscellanea

11.1. The Becker

Doring Equations

11.1.1. Well-Posedness

11.1.2. Long-Term Asymptotics

11.1.3. Decay Rates

11.2. Coagulation-Fragmentation with Diffusion.

Notes:

Includes bibliographical references and index.

ISBN:

9781498772655

149877265X

9780367235482

036723548X

OCLC:

1089881155

Publisher Number:

99988791733