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

@article{Epshteyn2022NonlinearIF,
  title={Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior},
  author={Yekaterina Epshteyn and Chang Liu and Ryan Chun-Fu Liu and Masashi Mizuno},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.09890}
}
. 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… 

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