Open AccessON THE NATURE OF A CLASSICAL PSEUDODIFFERENTIAL EQUATION
Author(s) -
В. А. Литовченко
Publication year - 2020
Publication title -
bukovinsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 2309-4001
DOI - 10.31861/bmj2020.02.07
Subject(s) - isotropy , cauchy distribution , generalization , operator (biology) , distribution (mathematics) , mathematics , mathematical analysis , work (physics) , initial value problem , gravitation , fokker–planck equation , mathematical physics , classical mechanics , physics , differential equation , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene
The work is devoted to the study of the general nature of one classical parabolic pseudodi-erential equation with the operator M.Rice of fractional dierentiation. At the correspondingvalues of the order of fractional dierentiation, this equation is also known as the isotropic superdiusion equation. It is a natural generalization of the classical diusion equation. It isalso known that the fundamental solution of the Cauchy problem for this equation is the densitydistribution of probabilities of stable symmetric random processes by P.Levy. The paper showsthat the fundamental solution of this equation is the distribution of probabilities of the force oflocal inuence of moving objects in a nonstationary gravitational eld, in which the interactionbetween masses is subject to the corresponding potential of M.Rice. In this case, the classicalcase of Newton’s gravity corresponds to the known nonstationary J.Holtsmark distribution.