Skip to content
Texas A&M University

Events for 10/13/2020 from all calendars

Nonlinear Partial Differential Equations

iCal  iCal

Time: 3:00PM - 00:00AM

Location: Zoom

Speaker: Azmy Ackleh, University of Louisiana at Lafayette

Title: A Structured Coagulation-Fragmentation Equation in the Space of Radon Measures: Unifying Discrete and Continuous Models

Abstract: Coagulation equations were introduced in the seminal works of Smoluchowski (1916) and (1917) in the discrete setting and extended to the continuous setting by Müller (1928). Later on Blatz and Tobolsky (1945), Melzak (1957) and others extended these equations to include fragmentation processes in discrete and continuous settings. In this talk, 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. We prove that the model is well-posed using a fixed-point approach. We also show that the model reduces to the classic discrete and continuous models for certain choices of parameters. We study the interplay between the physical processes of coagulation and fragmentation and biological processes including growth and reproduction to understand how these processes contribute to the regularity of solutions. We also present a numerical approximation for the coagulation-fragmentation equation in the space of Radon measures and test its performance.