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Entropy dissipation of Fokker-Planck equations on graphs

  • * Corresponding author: Wuchen Li

    * Corresponding author: Wuchen Li 
This work is partially supported by NSF Awards DMS-1419027, DMS-1620345, and ONR Award N000141310408.
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  • We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the space of probability measures supported on the nodes with respect to the discrete Wasserstein metric. The energy functional driving the gradient flow consists of a Boltzmann entropy, a linear potential and a quadratic interaction energy. We show that the solution converges to the Gibbs measures exponentially fast. The continuous analog of this asymptotic rate is related to the Yano's formula.

    Mathematics Subject Classification: Primary: 37C10; Secondary: 39B72.


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