Coagulation and diffusion: A probabilistic perspective on the Smoluchowski PDE
نویسندگان
چکیده
منابع مشابه
Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE
The Smoluchowski coagulation-diffusion PDE is a system of partial differential equations modelling the evolution in time of mass-bearing Brownian particles which are subject to shortrange pairwise coagulation. This survey presents a fairly detailed exposition of the kinetic limit derivation of the Smoluchowski PDE from a microscopic model of many coagulating Brownian particles that was undertak...
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The Smoluchowski coagulation equation is a mean-field model for the growth of clusters (particles, droplets,...) by binary coalescence, that is, the driving growth mechanism is the merger of two particles into a single one. In the simple situation where each particle is fully identified by its volume, it describes the dynamics of the volume distribution function f = f(t, x) ≥ 0 of particles of ...
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We establish the well-posedness of the Cauchy problem for the Smoluchowski coagulation equation in the homogeneous space L̇1 for a class of homogeneous coagulation rates of degree λ ∈ [0, 2). For any initial datum fin ∈ L̇1 we build a weak solution which conserves the mass when λ ≤ 1 and loses mass in finite time (gelation phenomena) when λ > 1. We then extend the existence result to a measure fr...
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ژورنال
عنوان ژورنال: Probability Surveys
سال: 2017
ISSN: 1549-5787
DOI: 10.1214/15-ps263