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Equilibria of aggregation-diffusion models with nonlinear potentials

math.AP · 2025-08-28 · accept · novelty 7.0

For aggregation-diffusion equations with nonlinear (s,p) Riesz potentials, radial stationary states coincide (up to scaling) with extremals of a Hardy-Littlewood-Sobolev inequality, and as s tends to 0 they converge to a ball in the diffusion-dominated case.

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  • Equilibria of aggregation-diffusion models with nonlinear potentials math.AP · 2025-08-28 · accept · none · ref 5

    For aggregation-diffusion equations with nonlinear (s,p) Riesz potentials, radial stationary states coincide (up to scaling) with extremals of a Hardy-Littlewood-Sobolev inequality, and as s tends to 0 they converge to a ball in the diffusion-dominated case.