| Abstract: |
| Persistent random walks exhibit the distinctive feature that fractionation occurs only when both heterogeneity and anisotropy are present. In this talk, we consider a discrete kinetic model derived from such a system, consisting of four linear inhomogeneous equations on a two-dimensional torus. We establish the existence and uniqueness of a weak solution, together with an energy-type inequality. We then show that as a small parameter tends to zero, the sum of the four components of the solution converges to the solution of a parabolic initial value problem governed by a heterogeneous diffusion equation, thereby providing a rigorous connection between the kinetic model and macroscopic fractionation phenomena. This is joint work with Danielle Hilhorst and Ho-Youn Kim |
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