Existence and uniqueness of solutions of Smoluchowski’s coagulation equation with source terms

Shirvani, M.; Van Roessel, H. J.

doi:10.1090/qam/1878265

Authors: M. Shirvani and H. J. Van Roessel
Journal: Quart. Appl. Math. 60 (2002), 183-194
MSC: Primary 82D60; Secondary 34C60, 82C05
DOI: https://doi.org/10.1090/qam/1878265
MathSciNet review: MR1878265
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Abstract: We prove the existence and uniqueness of a solution to the Smoluchowski coagulation equation with source terms. The coagulation equation with source terms is potentially useful in applications because one sometimes tries to control coagulation processes by the introduction of particles of various sizes into the system. The existence proof given here differs in style from most other existence proofs in two respects. First, it is not based on a finite-dimensional truncation of the coagulation equation; and secondly, it is achieved with a weaker hypothesis than is usually assumed on the initial data.

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