Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows

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dc.contributor.authorCherniha, Romanen_US
dc.contributor.authorKing, John en_US
dc.date.accessioned2025-11-19T06:36:04Z
dc.date.available2025-11-19T06:36:04Z
dc.date.issued2024
dc.description.abstractA wide class of two-component evolution systems is constructed admitting an infinite-dimensional Lie algebra. Some examples of such systems that are relevant to reaction–diffusion systems with cross-diffusion are highlighted. It is shown that a nonlinear evolution system related to the Ricci flow on warped product manifold, which has been extensively studied by several authors, follows from the above-mentioned class as a very particular case. The Lie symmetry properties of this system and its natural generalization are identified and a wide range of exact solutions is constructed using the Lie symmetry obtained. Moreover, a special case is identified when the system in question is reducible to the fast diffusion equation in one space dimension. Finally, another class of two-component evolution systems with an infinite-dimensional Lie symmetry that possess essentially different structures is presented. en_US
dc.identifier.citationCherniha R. Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows / Roman Cherniha, John R. King // Studies in Applied Mathematics. - 2024. - Vol. 153, issue 3. - Article e12737. - https://doi.org/10.1111/sapm.12737 en_US
dc.identifier.issn1467-9590
dc.identifier.issn0022-2526
dc.identifier.urihttps://doi.org/10.1111/sapm.12737
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/37604
dc.language.isoen en_US
dc.relation.sourceStudies in Applied Mathematics en_US
dc.statusfirst published en_US
dc.subjectexact solution en_US
dc.subjectLie symmetry en_US
dc.subjectnonlinear PDE en_US
dc.subjectRicci flow en_US
dc.subjectarticle en_US
dc.titleNonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows en_US
dc.typeArticle en_US
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