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Asymptotic localization
in multicomponent mass conserving coagulation equations
Marina A. Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez |
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Vol. 6 (2024), No. 3, 731–764
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Abstract |
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We prove that the time-dependent solutions of a large class of Smoluchowski coagulation equations for multicomponent systems concentrate along a particular direction of the space of cluster compositions for long times. The direction of concentration is determined by the initial distribution of clusters. These results allow to prove the uniqueness and global stability of the self-similar profile with finite mass in the case of coagulation kernels which are not identically constant, but are constant along any direction of the space of cluster compositions. |
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Keywords
multicomponent Smoluchowski's equation, localization,
time-dependent solutions, self-similarity, stability
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Mathematical Subject Classification
Primary: 35Q82, 45K05
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Milestones
Received: 15 July 2023
Revised: 9 February 2024
Accepted: 25 April 2024
Published: 1 October 2024
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Authors |
| Marina A. Ferreira | ||
| Institut de Mathématiques de
Toulouse, UMR 5219, CNRS Toulouse France |
CMUC, Department of
Mathematics University of Coimbra Coimbra Portugal |
Department of Mathematics and
Statistics University of Helsinki Helsinki Finland |
| Jani Lukkarinen | ||
| Department of Mathematics and
Statistics University of Helsinki Helsinki Finland |
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| Alessia Nota | ||
| Department of Information
Engineering, Computer Science and Mathematics University of L’Aquila L’Aquila Italy |
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| Juan J. L. Velázquez | ||
| Institute for Applied
Mathematics University of Bonn Bonn Germany |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
