期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 266, 期 1, 页码 653-715出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.07.059
关键词
Linear Smoluchowski's equation; Coagulation dynamics; Long-time asymptotics; Self-similar profiles
类别
资金
- CRC 1060 The mathematics of emergent effects of the University of Bonn - German Science Foundation (DFG)
- Lichtenberg Professorship grant of the VolkswagenStiftung
In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law v(-sigma). The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent sigma > 3, but the model can be expected to be valid, on heuristic grounds, for sigma > 5/3. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent sigma. Here we show that for 5/3 < sigma < 2 the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable. (C) 2018 Elsevier Inc. All rights reserved.
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