Asymptotic behavior for a coalescence problem

Bruno, Oscar; Friedman, Avner; Reitich, Fernando

doi:10.1090/S0002-9947-1993-1145729-6

Asymptotic behavior for a coalescence problem
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by Oscar Bruno, Avner Friedman and Fernando Reitich PDF

Trans. Amer. Math. Soc. 338 (1993), 133-158 Request permission

Abstract:

Consider spherical particles of volume $x$ having paint on a fraction $y$ of their surface area. The particles are assumed to be homogeneously distributed at each time $t$, so that one can introduce the density number $n(x,y,t)$. When collision between two particles occurs, the particles will coalesce if and only if they happen to touch each other, at impact, at points which do not belong to the painted portions of their surfaces. Introducing a dynamics for this model, we study the evolution of $n(x,y,t)$ and, in particular, the asymptotic behavior of the mass $xn(x,y,t)dx$ as $t \to \infty$.

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