Stability problems arising in biologically motivated PDEs

Zoi Rapti
University of Illinois
Monday, November 30, 2020 - 12:00pm to 1:00pm
Via Zoom

In many biological models, including epidemic models for cholera and rabies and predator-prey models, the diffusivity properties of the various compartments may vary. In this work, we focus on situations where the mathematical model contains one diffusing compartment (PDE) that is coupled with other compartments that are modeled by ODEs. When studying the linear stability of steady states, one ends up with rational eigenvalue problems. The difficulty with these problems, from the point of view of both analysis and numerical experimentation, is that one has no apriori information as to where the spectrum of the problem might lie. Here, we show that a number of the properties of self-adjoint eigenvalue problems (including the reality of the spectrum) carry over to the operators considered in this work. Our analysis is based on the theory of Herglotz functions. Concrete applications will be demonstrated in models of rabies infection in fox populations, plant-herbivore interactions and morphogen diffusion.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8