Mathematics Seminar - Dr. Cordula Reisch, TU Braunschweig

Ttile: Nonlocality-induced instabilities in reaction-diffusion systems arising from modeling inflammation

Abstract:

Inflammations are complex processes that involve many cells acting on various spatial and temporal scales. Reaction-diffusion models provide a framework for studying the long-term behavior of infections by abstracting from the cell-scale. The abstraction of the tissue structure leads to nonlocal and heterogeneous reaction terms describing the inflow of immune cells into certain organ regions.  The parameter of the nonlocal term may change the dynamics such that the interpretation of solutions changes from persisting inflammation to healing infection courses.

More generally, the parameters of the nonlocal terms influence the stability of stationary states from stable behavior to instability. Starting from stable reaction diffusion equations without nonlocality, I present analytical and numerical results on instabilities induced by a heterogeneous nonlocal term in the reaction functions.