Uniqueness of Fat-Tailed Self-Similar Profiles to Smoluchowski's Coagulation Equation for a Perturbation of the Constant Kernel.

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Title page
Chapter 1. Introduction
1.1. Smoluchowski's equation
1.2. Long-time behaviour and self-similarity
1.3. The equation for self-similar profiles
1.4. Finite mass, fat-tailed profiles and scale invariance
1.5. Existence and uniqueness of self-similar profiles
1.6. The constant kernel =2
1.7. Assumptions on the kernel
1.8. Preliminary work and main result
1.9. The boundary layer at zero
1.10. Outline of the main ideas and strategy of the proof
Chapter 2. Functional setup and preliminaries
2.1. Function spaces and norms
2.2. Transforming the equation to Laplace variables
2.3. Notation and elementary properties of \T
Chapter 3. Uniqueness of profiles -Proof of Theorem 1.12
3.1. Key ingredients for the proof
3.2. Proof of Theorem 1.12
Chapter 4. Continuity estimates
4.1. Proof of \cref{Lem:est:Arho,Lem:est:B2}
4.2. Proof of Proposition 3.5
4.3. Estimates for differences -Proof of Proposition 3.6
Chapter 5. Linearised coagulation operator -Proof of Proposition 3.7
Chapter 6. Uniform bounds on self-similar profiles
6.1. A priori estimates for self-similar profiles
6.2. Uniform convergence in Laplace variables
6.3. Proof of \cref{Prop:norm:boundedness,Prop:closeness:two:norm}
Chapter 7. The boundary layer estimate
7.1. Boundary layer equation
7.2. Preliminary estimates
7.3. Proof of Proposition 3.10
Chapter 8. The representation formula for ₀(⋅, )
8.1. Analyticity properties
8.2. Proof of Proposition 7.11
Chapter 9. Integral estimate on \Qo₀(⋅, )
9.1. Proof of Proposition 7.12
Chapter 10. Asymptotic behaviour of several auxiliary functions
10.1. Bounds on moments
10.2. Asymptotic behaviour of _{ } and Φ
10.3. Regularity properties close to zero
Appendix A. Useful elementary results.

Appendix B. The representation formula for
B.1. Proof of Proposition 1.2
B.2. Integral estimates on \Ker
Appendix C. Existence of profiles
Acknowledgments
Bibliography
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