J 2022

Mapping method of group classification

OPANASENKO, Stanislav and Roman POPOVYCH

Basic information

Original name

Mapping method of group classification

Authors

OPANASENKO, Stanislav (804 Ukraine, guarantor) and Roman POPOVYCH (804 Ukraine, belonging to the institution)

Edition

Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2022, 0022-247X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Journal of Mathematical Analysis and Applications

RIV identification code

RIV/47813059:19610/22:A0000118

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1016/j.jmaa.2022.126209

UT WoS

000796260000001

Keywords in English

Lie symmetries; Group classification; Mapping method; Weakly similar classes; Fokker-Planck equations; Kolmogorov equations

Tags

Tags

International impact, Reviewed
Změněno: 9/3/2023 15:42, Mgr. Aleš Ryšavý

Abstract

V originále

We revisit the entire framework of group classification of differential equations. After introducing the notion of weakly similar classes of differential equations, we develop the mapping method of group classification for such classes, which generalizes all the versions of this method that have been presented in the literature. The mapping method is applied to group classification of various classes of Kolmogorov equations and of Fokker-Planck equations in the case of space dimension one. The equivalence groupoids and the equivalence groups of these classes are computed. The group classification problems for these classes with respect to the corresponding equivalence groups are reduced to finding all inequivalent solutions of heat equations with inequivalent potentials admitting Lie-symmetry extensions. This reduction allows us to exhaustively solve the group classification problems for the classes of Kolmogorov and Fokker-Planck equations with time-independent coefficients.
Displayed: 24/12/2024 03:42