| Abstract: |
| This study investigates the dynamic interactions between two populations coexisting within a shared spatial domain. We develop theoretical and numerical approaches to analyze situations in which one population must traverse a territory occupied by another, requiring strategies to mitigate congestion due to spatial limitations. Population 1 is modeled through a linear transport equation, while Population 2 is described by a granular diffusion model inspired by sandpile dynamics, capturing its internal reorganization and natural tendency to decongest. Numerical simulations are used to explore how different movement strategies adopted by the traversing population---such as directed motion toward a target, internal spreading to reduce local density, or uniform dispersion across the domain---influence the response and redistribution of the resident population. The results highlight how the interplay between transport and granular diffusion mechanisms shapes the global behavior of the system. |
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