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

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