Volume 55, Number 5, September-October 2021
|Page(s)||2473 - 2501|
|Published online||26 October 2021|
A structured coagulation-fragmentation equation in the space of radon measures: Unifying discrete and continuous models
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
2 Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Pabellón I, Ciudad Universitaria, Buenos Aires, Argentina
* Corresponding author: firstname.lastname@example.org
Accepted: 23 September 2021
We present a structured coagulation-fragmentation model which describes the population dynamics of oceanic phytoplankton. This model is formulated on the space of Radon measures equipped with the bounded Lipschitz norm and unifies the study of the discrete and continuous coagulation-fragmentation models. We prove that the model is well-posed and show it can reduce down to the classic discrete and continuous coagulation-fragmentation models. To understand the interplay between the physical processes of coagulation and fragmentation and the biological processes of growth, reproduction, and death, we establish a regularity result for the solutions and use it to show that stationary solutions are absolutely continuous under some conditions on model parameters. We develop a semi-discrete approximation scheme which conserves mass and prove its convergence to the unique weak solution. We then use the scheme to perform numerical simulations for the model.
Mathematics Subject Classification: 35L60 / 35Q92 / 92D25
Key words: Coagulation-fragmentation equations / structured populations / non-negative Radon measures / Bounded-Lipschitz norm / semi-discrete schemes / conservation of Mass
© The authors. Published by EDP Sciences, SMAI 2021
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