Dr. Satyajith Bommana Boyana (Florida Polytechnic University) will speak on "An Interface-Coupled Reaction–Diffusion–Advection Model for Population Persistence" at this week's seminar.
Abstract: Spatial heterogeneity and movement behavior play important roles in determining whether populations can persist in fragmented habitats. In particular, individuals may exhibit directed movement toward favorable environmental conditions, while their ability to move between adjacent habitats may depend on local population density and the properties of the interface separating them.
We develop a reaction–diffusion–advection model to investigate population persistence in two adjacent habitat patches with distinct movement mechanisms. The model incorporates spatially varying directed movement in one patch, random dispersal in both patches, and a nonlinear interface condition describing density-dependent migration. We discuss the biological motivation and conservation-based formulation of the model, along with a weak subsolution–supersolution framework for establishing existence and uniqueness of positive steady states. Through finite element simulations, we examine how directional movement and interface dynamics influence population distributions and persistence thresholds. Our numerical findings suggest that stronger directed movement can increase the minimum habitat size required for persistence, highlighting the complex interplay between dispersal behavior and habitat connectivity. This is a collaborative work with Keta Henderson, and Dustin Nichols.
Short Bio: Dr. Satyajith Bommana Boyana is an assistant professor in the Department of Applied Mathematics at Florida Polytechnic University. His research focuses on the development, implementation, and analysis of novel discontinuous Galerkin (DG) schemes, particularly in the context of optimization problems with inequality constraints that arise in many real-world applications such as inverse problems, computational fluid dynamics, engineering processes like cooling processes, shape optimization in aerodynamics, and more. He completed his Ph.D. in Computational Mathematics at the University of North Carolina at Greensboro. His current recent interests include mathematical ecology and physics-informed machine learning.
Read More