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

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Abstract

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.

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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

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