Session S01 - Modeling and Computation for Control and Optimization of Biological and Physical Systems

Thursday, July 15, 14:30 ~ 14:55 UTC-3

A size-structured coagulation-fragmentation model on the space of measures: well-posedness and numerical approximation

Azmy Ackleh

University of Louisiana at Lafayette, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We formulate a size-structured coagulation-fragmentation model on the space of Radon measures equipped with the bounded Lipschitz norm. Such formulation unifies the study of discrete and continuous coagulation-fragmentation models. We establish the well-posedness of this model and show that 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 then develop a numerical approximation scheme which conserves mass and prove its convergence to the unique weak solution.

Joint work with Rainey Lyons (University of Louisiana at Lafayette) and Nicolas Saintier (University of Buenos Aires).

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