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arXiv · 2206.09890

Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior

Yekaterina Epshteyn·Chang Liu·Chun Liu·Masashi Mizuno
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Abstract

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such nonstandard models by reformulating and extending the classical entropy method, under the assumption of periodic boundary condition. In addition, illustrative numerical tests are presented to highlight the essential points of the current analytical results and to motivate future analysis.

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Yekaterina Epshteyn, Chang Liu, Chun Liu, Masashi Mizuno. 2022-06-20. Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior. https://arxiv.org/abs/2206.09890

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