Geodesic
Solutions with peaks for a coagulation-fragmentation equation. Part II: Aggregation in peaks
Bonacini, Marco1 ; Niethammer, Barbara2 ; Velázquez, Juan J.L.2
1 a Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Povo (TN), Italy
2 b University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany
Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 601-646

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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. In a companion paper we constructed a two-parameter family of stationary solutions concentrated in Dirac masses, and we carefully studied the asymptotic decay of the tails of these solutions, showing that this behaviour is stable. In this 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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DOI : 10.1016/j.anihpc.2020.08.007
Keywords: Coagulation-fragmentation equation, Solutions with peaks, Stability, Aggregation

Bonacini, Marco 1 ; Niethammer, Barbara 2 ; Velázquez, Juan J.L. 2

1 a Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Povo (TN), Italy
2 b University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany 
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     title = {Solutions with peaks for a coagulation-fragmentation equation. {Part} {II:} {Aggregation} in peaks},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {601--646},
     publisher = {Elsevier},
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Bonacini, Marco; Niethammer, Barbara; Velázquez, Juan J.L. Solutions with peaks for a coagulation-fragmentation equation. Part II: Aggregation in peaks. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 601-646. doi: 10.1016/j.anihpc.2020.08.007

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