Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F24%3AA0000168" target="_blank" >RIV/47813059:19610/24:A0000168 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/10.1111/sapm.12695" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1111/sapm.12695</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1111/sapm.12695" target="_blank" >10.1111/sapm.12695</a>
Alternative languages
Result language
angličtina
Original language name
Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation
Original language description
Within the class of (1+2)-dimensional ultraparabolic linear equations, we distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the point equivalence, it is a unique equation within the class whose essential Lie invariance algebra is five-dimensional and nonsolvable. Using the direct method, we compute the point symmetry pseudogroup of this equation and analyze its structure. In particular, we single out its essential subgroup and classify its discrete elements. We exhaustively classify all subalgebras of the corresponding essential Lie invariance algebra up to inner automorphisms and up to the action of the essential point-symmetry group. This allowed us to classify Lie reductions and Lie invariant solutions of the equation under consideration. We also discuss the generation of its solutions using point and linear generalized symmetries and carry out its peculiar generalized reductions. As a result, we construct wide families of its solutions parameterized by an arbitrary finite number of arbitrary solutions of the (1+1)-dimensional linear heat equation or one or two arbitrary solutions of (1+1)-dimensional linear heat equations with inverse square potentials.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studies in Applied Mathematics
ISSN
0022-2526
e-ISSN
1467-9590
Volume of the periodical
153
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
30
Pages from-to
„e12695-1“-„e12695-30“
UT code for WoS article
001202807700001
EID of the result in the Scopus database
2-s2.0-85191006238