Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels

Citations of this article
Mendeley users who have this article in their library.


The uniqueness and existence of measure-valued solutions to Smoluchowski's coagulation equation are considered for a class of homogeneous kernels. Denoting by λ ∈ (-∞, 2]/{0} the degree of homogeneity of the coagulation kernel a, measure-valued solutions are shown to be unique under the sole assumption that the moment of order λ of the initial datum is finite. A similar result was already available for the kernels a (x, y) = 2, x + y and xy, and is extended here to a much wider class of kernels by a different approach. The uniqueness result presented herein also seems to improve previous results for several explicit kernels. Furthermore, a comparison principle and a contraction property are obtained for the constant kernel. © 2005 Elsevier Inc. All rights reserved.




Fournier, N., & Laurençot, P. (2006). Well-posedness of Smoluchowski’s coagulation equation for a class of homogeneous kernels. Journal of Functional Analysis, 233(2), 351–379. https://doi.org/10.1016/j.jfa.2005.07.013

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free