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Moment bounds for the Smoluchowski equation and their consequences

Abstract:

We prove L∞ bounds on moments Xa : = ∑ mεN ma fm(x,t) of the Smoluchowski coagulation equations with diffusion, in any dimension d ≥ 1. If the collision propensities α(n, m) of mass n and mass m particles grow more slowly than (n + m) (d(n) + d(m), and the diffusion rate d(̇) is non-increasing and satisfies m-b1 ≤ d(m) ≤ mb2 for some b 1 and b 2 satisfying 0 ≤ b 2 < b 1 < ∞, then any weak solution satisfies Xa ε L ℝ × [0,T] ∩ L1 ( ℝ × [0, T] for every a ∞ N and T (0, ∞), (provided that ...

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Publication status:
Published

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Publisher copy:
10.1007/s00220-007-0304-5

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Rezakhanlou, F More by this author
Journal:
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume:
276
Issue:
3
Pages:
645-670
Publication date:
2007-12-05
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
URN:
uuid:f00e1175-e768-4ac8-8eb2-9106890755f4
Source identifiers:
104558
Local pid:
pubs:104558
Language:
English

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