Nonlinear inhomogeneous Fokker-Planck models: Energetic-variational structures and long-time behavior
Nonlinear inhomogeneous Fokker-Planck models: Energetic-variational structures and long-time behavior
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非线性非齐次福克-普朗克模型：能量变分结构和长期行为
DOI：
10.1142/s0219530522400036
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发表时间：
2022
影响因子：
2.2
通讯作者：
Mizuno Masashi
中科院分区：
文献类型：
--
作者：
Epshteyn Yekaterina;Liu Chang;Liu Chun;Mizuno Masashi
受多晶材料中晶粒生长建模的启发，我们考虑了具有不均匀扩散和可变迁移率参数的非线性 Fokker-Plank 模型。在周期性边界条件的假设下，我们通过重新表述和扩展经典熵方法来开发此类非标准模型的大时间渐近分析。此外，还提供了说明性数值测试，以突出当前分析结果的要点并激发未来的分析。
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.