| Abstract: |
| Reaction-Diffusion equations have been applied rather successfully to model various biological/ecological phenomena. More recently, authors have begun to consider the influence of cognition (e.g., perception, memory, learning) in animal movement models. In many cases, this leads to non-standard reaction-diffusion-advection equations and systems that are both nonlocal (in space) and nonlinear at higher order. In this talk, I will explore some recent advances made in a single species animal movement model paired with a so-called cognitive map. For this session, I will focus on the existence of global weak solutions for two biologically reasonable scenarios featuring slightly different hypotheses. This is joint work with colleagues Di Liu, Jonathan Potts, Junping Shi and Hao Wang. |
|