Abstract
This paper concerns the proof of the exponential rate of convergence of the solution of a Fokker-Planck equation, with a drift term not being the gradient of a potential function and endowed by Robin type boundary conditions. This kind of problem arises, for example, in the study of interacting neurons populations. Previous studies have numerically shown that, after a small period of time, the solution of the evolution problem exponentially converges to the stable state of the equation.
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Carrillo, J.A., Mancini, S. & Tran, MB. On the Exponential Convergence Rate for a Non-Gradient Fokker-Planck Equation in Computational Neuroscience. J Elliptic Parabol Equ 1, 271–279 (2015). https://doi.org/10.1007/BF03377381
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DOI: https://doi.org/10.1007/BF03377381