Yahya Jaafra (An-Najah National University Nablus, Palestine): Stationary solutions of nonlocal interaction systems with nonlinear diffusion

Zoom Link:

https://uni-kassel.zoom-x.de/j/96217091997?pwd=RVRaVVBRclFJYU9jczNZSWF3SXI2QT09

Meeting ID: 962 1709 1997
Passcode: cauchy

Abstract:

I will present a work that studies stationary solutions of nonlocal interaction systems with nonlinear (quadratic) diffusion, motivated by predator-prey dynamics between two species. The model includes nonlocal attraction-repulsion potentials and self-interaction forces, leading to steady states formed by sums of Barenblatt-type profiles. Existence of such states is proven under small diffusion using the functional Implicit Function Theorem. Additionally, a one-dimensional model with porous-medium-type diffusion is analyzed, showing that solutions can either converge to steady states or decay to zero, depending on the initial data and the relation between diffusion strength and the interaction kernel. Numerical simulations support the theoretical findings.