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arXiv · 2504.10306

Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation

Marina A. Ferreira·Sakari Pirnes
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Abstract

Global solutions to the multicomponent Smoluchowski coagulation equation are constructed for measure-valued initial data with minimal assumptions on the moments. The framework is based on an abstract formulation of the Arzel\`a-Ascoli theorem for uniform spaces. The result holds for a large class of coagulation rate kernels, satisfying a power-law upper bound with possibly different singularities at small-small, small-large and large-large coalescence pairs. This includes in particular both mass-conserving and gelling kernels, as well as interpolation kernels used in applications. We also provide short proofs of mass-conservation and gelation results for any weak solution, which extends previous results for one-component systems.

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Marina A. Ferreira, Sakari Pirnes. 2025-04-14. Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation. https://arxiv.org/abs/2504.10306

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