Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials

2016/02/22 by José A. Carrillo, Yanghong Huang, Carrillo, José A. +1 · 2 citations
Mathematics · Medicine · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.1602.06615

openalex publication_date 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions of the aggregation equation with power-law kernels are constructed by inverting Fredholm integral operators or by employing certain integral identities. These solutions are expected to be the global energy stable equilibria and to characterize the generic behaviors of stationary solutions for more general interactions.

Cited by

• A family of interaction energy minimizers supported on two intervals
• Existence of minimizers for interaction energies with external potentials

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