scholarly journals Self-similar Solutions with Fat Tails for Smoluchowski’s Coagulation Equation with Locally Bounded Kernels

2012 ◽  
Vol 318 (2) ◽  
pp. 505-532 ◽  
Author(s):  
B. Niethammer ◽  
J. J. L. Velázquez
Keyword(s):  
Fat Tails ◽  
Coagulation Equation ◽  
Self Similar ◽  
Smoluchowski's Coagulation Equation ◽  
Similar Solutions

Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels

2006 ◽  
Vol 136 (3) ◽  
pp. 485-508 ◽  
Author(s):  
Nicolas Fournier ◽  
Philippe Laurençot
Keyword(s):  
Rigorous Proof ◽  
Singular Behaviour ◽  
Coagulation Equation ◽  
Local Properties ◽  
Self Similar ◽  
Smoluchowski's Coagulation Equation ◽  
Similar Solutions ◽  
Coagulation Kernel

The regularity of the scaling profiles ψ to Smoluchowski’s coagulation equation is studied when the coagulation kernel K is given by K(x, y) = xλ + yλ with λ∈ (0, 1). More precisely, ψ is C1-smooth on (0,∞) and decays exponentially fast for large x. Furthermore, the singular behaviour of ψ(x) as x → 0 is identified, thus giving a rigorous proof of physical conjectures.

scholarly journals Self-similar solutions with fat tails for a coagulation equation with nonlocal drift

2009 ◽  
Vol 347 (15-16) ◽  
pp. 909-914 ◽  
Author(s):  
Michael Herrmann ◽  
Philippe Laurençot ◽  
Barbara Niethammer
Keyword(s):  
Fat Tails ◽  
Coagulation Equation ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Uniqueness of fat-tailed self-similar profiles to Smoluchowski’s coagulation equation for a perturbation of the constant kernel

2021 ◽  
Vol 271 (1328) ◽  
Author(s):  
Sebastian Throm
Keyword(s):  
Difficult Problem ◽  
Fat Tails ◽  
Algebraic Decay ◽  
Content Type ◽  
Similar Profile ◽  
Tail Behaviour ◽  
Coagulation Equation ◽  
Self Similar ◽  
Smoluchowski's Coagulation Equation

This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski’s coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel K K which can be written as K = 2 + ε W K=2+\varepsilon W . The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on W W , we will show that for sufficiently small ε \varepsilon there exists, up to normalisation of the tail behaviour at infinity, at most one self-similar profile. Establishing uniqueness of self-similar profiles for Smoluchowski’s coagulation equation is generally considered to be a difficult problem which is still essentially open. Concerning fat-tailed self-similar profiles this article actually gives the first uniqueness statement for a non-solvable kernel.

scholarly journals Self-similar solutions with fat tails for a coagulation equation with diagonal kernel

2011 ◽  
Vol 349 (9-10) ◽  
pp. 559-562 ◽  
Author(s):  
Barbara Niethammer ◽  
Juan J.L. Velázquez
Keyword(s):  
Fat Tails ◽  
Coagulation Equation ◽  
Self Similar ◽  
Similar Solutions
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