On the Exponential Convergence Rate for a Non-Gradient Fokker-Planck Equation in Computational Neuroscience

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 neur...

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Bibliographic Details
Published in:Journal of elliptic and parabolic equations 2015-10, Vol.1 (2), p.271-279
Main Authors: Carrillo, J. A., Mancini, S., Tran, M.-B.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary: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.
ISSN:2296-9020
2296-9039
DOI:10.1007/BF03377381