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On self-similarity and stationary problem for fragmentation and coagulation
| Citations: | 47 - 9 self |
BibTeX
@MISC{Escobedo_onself-similarity,
author = {M. Escobedo and S. Mischler and M. Rodriguez Ricard},
title = {On self-similarity and stationary problem for fragmentation and coagulation},
year = {}
}
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Abstract
We prove the existence of a stationary solution of any given mass to the coagulationfragmentation equation without assuming a detailed balance condition, but assuming instead that aggregation dominates fragmentation for small particles whisle fragmentation predominates for large particles. We also show the existence of a self similar solution of any given mass to the coagulation equation and to the fragmentation equation for kernels satisfying a scaling property. These results are obtained by applying a simple abstract result of functional analysis based on the Tykhonov fixed point theorem, and which slightly generalizes a method introduced in [26]. Moreover, we show that the solutions to the fragmentation equation with initial data of a given mass behaves, as t → +∞, as the self similar solution of the same mass. 1 Introduction and
Keyphrases
stationary problem fragmentation equation self similar solution detailed balance condition large particle point theorem initial data scaling property small particle coagulation equation fragmentation predominates simple abstract result mass behaves coagulationfragmentation equation functional analysis stationary solution
