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

Authors:
M. Shirvani;H. J. Van Roessel
Affiliations:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada;Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada
Venue:
Quarterly of Applied Mathematics
Year:
2002

Citing 2
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The mass-conserving solutions of Smoluchowski's coagulation equation: the general bilinear kernel

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

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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.