Analytic methods for coagulation-fragmentation models. Volume II /
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| Main Authors: | , , |
|---|---|
| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
[2020]
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| Series: | Monographs and research notes in mathematics.
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| Subjects: | |
| Online Access: | Connect to this title online (unlimited simultaneous users allowed; 325 uses per year) |
Table of 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. 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. Constant Coagulation Kernel k(x, y) = 2
- 10.2.2. Additive Coagulation Kernel k+(x, y) = x + y
- 10.2.3. Diagonal Coagulation Kernel k(x, y) = r(x)δx-y
- 10.2.4. Mass-Conserving Self-Similar Profiles
- 10.2.4.1. 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. 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. 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.