Journal
KINETIC AND RELATED MODELS
Volume 11, Issue 4, Pages 933-952Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2018037
Keywords
Coagulation equation; diagonal kernel; long-time behaviour; oscillations
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Funding
- CRC The mathematics of emergent effects at the University of Bonn - German Science Foundation (DFG)
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We characterize the long-time behaviour of solutions to Smoluchowski's coagulation equation with a diagonal kernel of homogeneity gamma < 1. Due to the property of the diagonal kernel, the value of a solution at a given cluster size depends only on a discrete set of points. As a consequence, the longtime behaviour of solutions is in general periodic, oscillating between different rescaled versions of a self-similar solution. Immediate consequences of our result are a characterization of the set of data for which the solution converges to self-similar form and a uniqueness result for self-similar profiles.
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