Integral methods for solving Fokker-Planck-type equations

Conference · Mon Jan 01 04:00:00 EST 1990

OSTI ID:6999986

Protopopescu, V

Fokker-Planck-type equations occur quite often in different domains of physics and applied mathematics as various realizations of a generic degenerate parabolic equation. Even in the simplest situations, the analysis of the general Fokker-Planck equation is difficult and has been mostly confined to linear case, where partial results have been obtained in showing existence, uniqueness, regularity, and completeness of eigenfunctions. In the present paper, we present a canonical integral approach that solves, in principle, the most general linear or nonlinear Fokker-Planck-type equations. The method is formal in the sense that it does not provide per se the means to prove existence and uniqueness of the solution in an abstract setting. The formalism is based on the Green's functions and their natural extensions to nonlinear systems and allows one to compute the solution (assumed to exist uniquely), by using a canonical iterative scheme. We present several applications of the integral approach in connection with previously developed methods and results. 26 refs.

• Research Organization: Oak Ridge National Lab., TN (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6999986
• Report Number(s): CONF-9005223-1; ON: DE90012171
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700103* -- Fusion Energy-- Plasma Research-- Kinetics
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
EQUATIONS
FOKKER-PLANCK EQUATION
FUNCTIONS
GREEN FUNCTION
INTEGRAL EQUATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS