Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 45, Issue 5, Pages 351-391Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2019.1684943
Keywords
Coagulation-fragmentation; exponential tails; long-time asymptotics; peak formation
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Funding
- German Science Foundation (DFG) [CRC 1060]
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The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the fragmentation kernel is diagonal. We construct a two-parameter family of stationary solutions concentrated in Dirac masses. We carefully study the asymptotic decay of the tails of these solutions, showing that this behavior is stable. In a companion paper, we prove that for initial data which are sufficiently concentrated, the corresponding solutions approach one of these stationary solutions for large times.
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