| Abstract: |
| This talk introduces a new class of cross-diffusion systems designed to study the dispersal of species under overcrowding constraints. Moving beyond classical $W_2-$Wasserstein flows or standard PDE couplings, we propose an approach based on proximal energy minimization through a minimum flow process. This framework allows us to establish a well-posed PDE system that captures the delicate interplay between diffusion and concentration gradients. Specifically, for homogeneous cases, we derive a well-defined PDE grounded in a novel $H^{-1}-$theory specifically developed for overcrowding dispersal. |
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