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

被引：2

作者：

Epshteyn, Yekaterina ^{[1
]}

Liu, Chang ^{[1
]}

Liu, Chun ^{[2
]}

Mizuno, Masashi ^{[3
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] IIT, Dept Appl Math, Chicago, IL 60616 USA

[3] Nihon Univ, Coll Sci & Technol, Dept Math, Tokyo 1018308, Japan

来源：

ANALYSIS AND APPLICATIONS | 2022年 / 20卷 / 06期

关键词：

Nonlinear Fokker-Planck equation; inhomogeneous diffusion; variable mobility; large time asymptotic analysis; entropy methods; free energy; finite-volume solution; DYNAMIC LATTICE MISORIENTATIONS; MEAN-CURVATURE FLOW; GRAIN-BOUNDARIES; MOTION; CONVERGENCE; EQUILIBRIUM; EQUATION;

D O I：

10.1142/S0219530522400036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1295 / 1356

页数：62

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