The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in a regime of large-distance interactions; they have been derived in the many-particle limit from moderately interacting particle systems with Lévy noise. The existence proof is based on a three-level approximation scheme, entropy and moment estimates, and a new Aubin-Lions compactness lemma in the whole space.
Analysis of a fractional cross-diffusion system for multi-species populations
27.10.2021 14:00 - 14:45
Organiser:
SFB 65, DK
Location:
Zoom Meeting
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- pde_afternoon_2021-10-27.pdf 597 KB