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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Asymptotic behavior for a coalescence problem


Authors: Oscar Bruno, Avner Friedman and Fernando Reitich
Journal: Trans. Amer. Math. Soc. 338 (1993), 133-158
MSC: Primary 35Q99; Secondary 35B40, 35R10, 82C99
DOI: https://doi.org/10.1090/S0002-9947-1993-1145729-6
MathSciNet review: 1145729
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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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DOI: https://doi.org/10.1090/S0002-9947-1993-1145729-6
Keywords: Particles, collision, coalescence, asymptotic behavior
Article copyright: © Copyright 1993 American Mathematical Society

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