Keller-Segel type systems are important models with many applications in biology, engineering
and physics. The Poisson-Nernst-Planck (PNP) system is a well-known model of ion transport, which belongs to Keller-Segel type systems and plays a crucial role in the study of many physical and biological phenomena. Cross-diffusion terms may describe the exclusion of steric effects. In this lecture,
I shall introduce cross diffusion terms from the Lennard-Jones potential and show the analytical results as follows:
1. Traveling wave solutions of a two-species chemotaxis model.
2. Stability of 1D boundary layer solutions to PNP systems.