Solutions with peaks for a coagulation-fragmentation equation. Part II: Aggregation in peaks |
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| Authors: | Marco Bonacini Barbara Niethammer Juan JL Velázquez |
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| Institution: | 1. Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Povo (TN), Italy;2. University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany;1. EPFL SB, Station 8, CH-1015 Lausanne, Switzerland;2. Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland;3. IMATI-CNR, via Ferrata 5, I-27100 Pavia, Italy;1. Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique, Sorbonne Université, 4 Place Jussieu, 75252 Paris, France;2. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, PR China;1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, People''s Republic of China;2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Republic of China;3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People''s Republic of China |
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| Abstract: | 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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| Keywords: | Coagulation-fragmentation equation Solutions with peaks Stability Aggregation |
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