The continuous Redner-Ben-Avraham-Kahng coagulation system: Well-posedness and asymptotic behaviour

Pratibha Verma; Ankik Kumar Giri; F. P. da Costa

doi:10.3934/eect.2023010

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2023, Volume 12, Issue 5: 1247-1267. Doi: 10.3934/eect.2023010

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The continuous Redner-Ben-Avraham-Kahng coagulation system: Well-posedness and asymptotic behaviour

1.
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
2.
Departamento de Ciências e Tecnologia, Universidade Aberta, and Centre for Mathematical, Analysis, Geometry, and Dynamical Systems, IST, Universidade de Lisboa, Portugal

^*Corresponding author: Ankik Kumar Giri
^*Corresponding author: Ankik Kumar Giri

Received: August 2022

Revised: February 2023

Early access: March 2023

Published: October 2023

The first author is supported by the Council of Scientific and Industrial Research (CSIR), India. The third author is partially supported by the Fundação para a Ciência e Tecnologia (FCT), Portugal.

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Abstract

This paper examines the existence of solutions to the continuous Redner-Ben-Avraham-Kahng coagulation system under specific growth conditions on unbounded coagulation kernels at infinity. Moreover, questions related to uniqueness and continuous dependence on the data are also addressed under additional restrictions. Finally, the large-time behaviour of solutions is also investigated.

Keywords:

Coagulation,
Redner–Ben-Avraham–Kahng coagulation system,
existence,
uniqueness,
large-time behaviour.

Mathematics Subject Classification: Primary: 45J05, 45K05, 45G99, 45G10, 47G20; Secondary: 34K30.

Citation:

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Figure 1. Regions $ R_j $ where $ \tilde{\phi}(\varsigma, \varrho) $ has constant values

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References

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