Geometry and conservation laws for a class of second-order parabolic equations ii: conservation laws

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dc.contributor.authorMcMillan, B.B.
dc.date.issued2021
dc.description.abstractI consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservation laws of a given parabolic equation. This is used to show that conservation laws for any evolutionary parabolic equation depend on at most second derivatives of solutions. As a corollary, it is shown that the only evolutionary parabolic equations with at least one non-trivial conservation law are of Monge-Ampère type.
dc.description.statementofresponsibilityBenjamin B. McMillan
dc.identifier.citationSymmetry, Integrability and Geometry: Methods and Applications, 2021; 17:1-24
dc.identifier.doi10.3842/SIGMA.2021.047
dc.identifier.issn1815-0659
dc.identifier.issn1815-0659
dc.identifier.urihttp://hdl.handle.net/2440/131197
dc.language.isoen
dc.publisherInstitute of Mathematics NAS of Ukraine
dc.relation.granthttp://purl.org/au-research/grants/arc/DP190102360
dc.rightsCopyright status unknown
dc.source.urihttps://doi.org/10.3842/sigma.2021.047
dc.subjectConservation laws; parabolic symbol PDEs; Monge{Ampere equations; characteristic cohomology of exterior di erential systems
dc.titleGeometry and conservation laws for a class of second-order parabolic equations ii: conservation laws
dc.typeJournal article
pubs.publication-statusPublished

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