A structured coagulation-fragmentation equation in the space of radon measures: Unifying discrete and continuous models

• Autores: Ackleh, Azmy S.; Lyons, Rainey; Saintier, Nicolas Bernard Claude
• Año de publicación: 2021
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: BOUNDED-LIPSCHITZ NORM; COAGULATION-FRAGMENTATION EQUATIONS; CONSERVATION OF MASS; NON-NEGATIVE RADON MEASURES; SEMI-DISCRETE SCHEMES; STRUCTURED POPULATIONS
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Ackleh, Azmy S.. State University of Louisiana; Estados Unidos
Fil: Lyons, Rainey. State University of Louisiana; Estados Unidos
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina