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Asymptotic localization in multicomponent mass conserving coagulation equations

Marina A. Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez

Vol. 6 (2024), No. 3, 731–764
Abstract

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.

Keywords
multicomponent Smoluchowski's equation, localization, time-dependent solutions, self-similarity, stability
Mathematical Subject Classification
Primary: 35Q82, 45K05
Milestones
Received: 15 July 2023
Revised: 9 February 2024
Accepted: 25 April 2024
Published: 1 October 2024
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
Alessia Nota
Department of Information Engineering, Computer Science and Mathematics
University of L’Aquila
L’Aquila
Italy
Juan J. L. Velázquez
Institute for Applied Mathematics
University of Bonn
Bonn
Germany