The Annals of Applied Probability

Smoluchowski's coagulation equation: uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent

James R. Norris

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Abstract

Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of nonuniqueness is constructed. The stochastic coalescent is shown to converge weakly to the solution of Smoluchowski's equation.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 1 (1999), 78-109.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962598

Digital Object Identifier
doi:10.1214/aoap/1029962598

Mathematical Reviews number (MathSciNet)
MR1682596

Zentralblatt MATH identifier
0944.60082

Subjects
Primary: 82C21: Dynamic continuum models (systems of particles, etc.)
Secondary: 60H35: Computational methods for stochastic equations [See also 65C30]

Keywords
Smoluchowski's coagulation equation stochastic coalescent hydrodynamic limit

Citation

Norris, James R. Smoluchowski's coagulation equation: uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent. Ann. Appl. Probab. 9 (1999), no. 1, 78--109. doi:10.1214/aoap/1029962598. https://projecteuclid.org/euclid.aoap/1029962598


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References

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