Nonlinear aggregation-diffusion equations with Riesz potentials

Yanghong Huang, Edoardo Mainini, Juan Luis Vázquez, Bruno Volzone

Research output: Contribution to journalArticlepeer-review


We consider an aggregation-diffusion model, where the diffusion is nonlinear of porous medium type and the aggregation is governed by the Riesz potential of order s.  The addition of a quadratic diffusion term produces a more precise competition with the aggregation term for small s, as they have the same scaling if s = 0. We prove existence and uniqueness of stationary states and we characterize their asymptotic behavior as s goes to zero. Moreover, we prove existence of gradient flow solutions to the evolution problem by applying the JKO scheme.
Original languageEnglish
JournalJournal of Functional Analysis
Publication statusAccepted/In press - 11 Apr 2024


  • Aggregation-diffusion model
  • gradient flow
  • stationary states
  • Riesz potential


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