In the first part of this presentation, we consider a nonlocal advection model for two populations. We construct an energy functional to investigate the asymptotic behavior of the solution. To resolve the lack of compactness of the positive orbit, we use the narrow convergence in the space of Young measures through which we obtain a description of the asymptotic behavior of solutions. The numerical simulations confirm and complement our theoretical results. 

 

In the second part of this presentation, we consider a cell-cell repulsion population dynamic model based on a hyperbolic Keller-Segel equation with two populations. With the notion of solutions integrated along the characteristics, we prove the existence and uniqueness of solutions and the segregation property of two species. From a numerical perspective, we can also observe that the model admits a competitive exclusion principle (the results are different from the corresponding ODE model). More importantly, our model shows the complexity of the short term (6 days) co-cultured cell distribution depending on the initial distribution of each species.