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arXiv · 2506.08017

Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach

Masato Kimura·Hisanori Miyata
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Abstract

The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may exhibit a gelation phenomenon-a sudden loss of mass-when the coagulation kernel grows superlinearly. In this paper, we rigorously analyze mass conservation and gelation for weak solutions to the SCE with inhomogeneous coagulation kernels. By introducing a generalized moment framework, we derive sharp sufficient conditions for both mass conservation and gelation, expressed in terms of the initial data and the properties of the coagulation kernel.

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Masato Kimura, Hisanori Miyata. 2025-05-15. Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach. https://arxiv.org/abs/2506.08017

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