Mapping method of group classification

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F22%3AA0000118" target="_blank" >RIV/47813059:19610/22:A0000118 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X22002232" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X22002232</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126209" target="_blank" >10.1016/j.jmaa.2022.126209</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mapping method of group classification

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Mapping method of group classification

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

513

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

„126209-1“-„126209-43“

Kód UT WoS článku

000796260000001

EID výsledku v databázi Scopus

2-s2.0-85129246960