CONSTRUCTIVE SCHEME FOR VARIATIONAL-PRINCIPLES - THE BATEMAN PROCEDURE FOR KINETIC-EQUATIONS

The present paper is concerned with a systematic generalization of the local Lagrange formalism of first order. It is demonstrated how the h eat conduction equation, the Fokker-Planck equation, the linearized Bo ltzmann equation, and an extended nonlinear Boltzmann equation can be derived using the concept of nonlocal Lagrange formalism. These equati ons are produced as Euler-Lagrange equations by means of a variational principle. It turns out that the nonlocal methods are necessary from the very beginning. Nevertheless, within the framework of Frechet's fo rmalism the calculations are as easy as in the classical local case. T he investigations are based on a constructive scheme for finding gener al variational principles. This helpful tool is based on an idea origi nally proposed by Bateman.