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

We consider self-similar solutions of Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $γ< 1$. We show that there exists a family of second-kind self-similar solutions with power-law behavior $x^{-(1+ρ)}$ as $x \to \infty$ with $ρ\in (γ,1)$. To our knowledge this is the first example of a non-solvable kernel for which the existence of such a family has been established.

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