Steady States of Fokker-Planck Equations: I. Existence

Huang Wen; Ji Min; Liu Zhenxin; Yi Yingfei

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Steady States of Fokker-Planck Equations: I. Existence

机译：福克-普朗克方程的稳态：I.存在

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This is the first paper in a series concerning the study of steady states of a Fokker-Planck equation in a general domain in with drift term and diffusion term for any . In this paper, by using the level set method especially the integral identity which we introduced in Huang et al. (Ann Probab, 2015), we obtain several new existence results of steady states, including stationary solutions and measures, of the Fokker-Planck equation with non-degenerate diffusion under Lyapunov-like conditions. As applications of these results, we give some examples on the noise stabilization of an unstable equilibrium and the existence and uniqueness of steady states subject to boundary degeneracy of diffusion in a bounded domain.

机译：这是有关Fokker-Planck方程在任何漂移项和扩散项的一般域中的稳态研究的系列文章中的第一篇。在本文中，通过使用水平集方法，特别是我们在Huang等人中介绍的积分身份。（Ann Probab，2015），我们获得了在Lyapunov类条件下具有非退化扩散的Fokker-Planck方程的稳态的一些新存在结果，包括平稳解和测度。作为这些结果的应用，我们给出一些关于不稳定平衡的噪声稳定以及在有界域中受扩散边界退化影响的稳态的存在和唯一性的示例。

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来源
《Journal of dynamics and differential equations》 |2015年第4期|721-742|共22页
作者
Huang Wen; Ji Min; Liu Zhenxin; Yi Yingfei;
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作者单位

Chinese Acad Sci, USTC, Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China;

Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China;

Jilin Univ, Sch Math, Changchun 130012, Peoples R China;

Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada|Jilin Univ, Sch Math, Changchun 130012, Peoples R China|Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA;

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正文语种 eng
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关键词
Fokker-Planck equation; Existence; Stationary solution; Stationary measure; Integral identity; Level set method;

机译：福克-普朗克方程;存在性;平稳解;平稳测度;积分恒等式;水平集方法;

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专利

1. Steady States of Fokker-Planck Equations: II. Non-existence [J] . Huang Wen, Ji Min, Liu Zhenxin, Journal of dynamics and differential equations . 2015,第3a4期

机译：福克-普朗克方程的稳态：II。不存在
2. The existence of a solution with finite Dirichlet integral for the steady Navier-Stokes equations in a plane exterior symmetric domainThe existence of a solution with finite Dirichlet integral for the steady Navier-Stokes equations in a plane exterior symmetric domain [J] . Mikhail Korobkov, Konstantin Pileckas, Remigio Russo Journal de Mathematiques Pures et Appliquees . 2014,第3期

机译：平面外部对称域中稳定Navier-Stokes方程的有限Dirichlet积分解的存在性平面外部对称域中稳定Navier-Stokes方程的有限Dirichlet积分解的存在
3. Existence of periodic probability solutions to Fokker-Planck equations with applications [J] . Ji Min, Qi Weiwei, Shen Zhongwei, Journal of Functional Analysis . 2019,第11期

机译：与应用的Fokker-Planck方程的周期性概率解决方案存在
4. On explicit steady-state solutions of Fokker-Planck equations for a class of nonlinear feedback systems [C] . Brockett, R.W., Liberzon, . 1998

机译：一类非线性反馈系统Fokker-Planck方程的显式稳态解
5. Existence and Stability of Vortex Sheets and Entropy Waves for the Euler Equations for Steady Compressible Flows. [D] . Kukreja, Vaibhav. 2012

机译：稳态可压缩流的Euler方程的涡旋片和熵波的存在和稳定性。
6. Phase space volume scaling of generalized entropies and anomalous diffusion scaling governed by corresponding non-linear Fokker-Planck equations [O] . Dániel Czégel, Sámuel G. Balogh, Péter Pollner, -1

机译：由相应的非线性Fokker-Planck方程控制的广义熵的相空间体积缩放和反常扩散缩放
7. Stability of steady states in kinetic Fokker-Planck equations for Bosons and Fermions [O] . Neumann, Lukas, Sparber, Christof 2007

机译：Bosons动力学Fokker-planck方程稳态的稳定性和费米子
8. Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations. [R] . Renardy, M. 1984

机译：具有微分本构方程的粘弹性流体缓慢稳态流动的存在性。

Steady States of Fokker-Planck Equations: I. Existence

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