Institut für Mathematik
Dynamics of Nonlocal PDEs
Recently, nonlocality has emerged as a highly active theme in differential equations. In my talk, I shall give several examples of PDEs, where nonlocal effects play a, sometimes quite surprising, role. I am going to focus on elementary examples of one-dimensional reaction-diffusion equations. We start with dynamics of the FKPP equation with nonlocal convolution terms, then consider nonlocal modulation equations with convolution terms, and then proceed to waves in the fractional-diffusion Nagumo equation. Having illustrated the deterministic PDE case, we also provide one stochastic example, where nonlocality plays a key role in the context of neural fields in the cortex.
Senka Haznadar (senka [dot] omerhodzic [at] aau [dot] at)