Engineering Mechanics

Proceedings Vol. 11 (2005)

ENGINEERING MECHANICS 2005

Copyright © 2005 Institute of Mechanics of Solids, Faculty of Mechanical Engineering, Bruno University of Technology, Brno

 

Náprstek J.
pages 231 - +12p., full text

Fokker-Planck equation is a parabolic partial difierential equation describing the response probability density function of the dynamic system being excited by additive and/or multiplicative random processes of Gaussian and other types. When a non-stationary solution is necessary to be looked for, the method of separation of time and space coordinates can be used. This procedure leads to problem of eigen-values and eigenfunctions of the F okker-Planck operator. The non-symmetry and a number of other properties of this operator should be respected and carefully analysed, before the eigenfunction series as solution basis can be constructed and applied. The most important problems concerning the eigen-values and functions of the FP operator for one and multidimensional F P equation are discussed. Problems of the asymptotic convergence related with stationary solution existence and on the other hand prospective system metastability are analysed. Several illustrative examples of detailed analysis are presented.

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