scholarly journals Stability and Uniqueness of Self-similar Profiles in $$L^1$$ Spaces for Perturbations of the Constant Kernel in Smoluchowski’s Coagulation Equation

2021 ◽  
Vol 383 (3) ◽  
pp. 1361-1407
Author(s):  
Sebastian Throm
Keyword(s):  
Coagulation Equation ◽  
Self Similar ◽  
Smoluchowski's Coagulation Equation

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.

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