Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels
Nicolas Fournier, Philippe Laurençot · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2006
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 ) = x λ + y λ with λ∈ (0, 1). More precisely, ψ is C 1 -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.