Hierarchy of Conservation Laws of Diffusion--Convection Equations

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dc.creatorPopovych, Roman O.
dc.creatorIvanova, Nataliya M.
dc.date2004-07-06
dc.date2005-04-03
dc.date.accessioned2026-07-07T04:31:18Z
dc.date.available2026-07-07T04:31:18Z
dc.descriptionWe introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0407008
dc.identifierhttp://arxiv.org/abs/math-ph/0407008
dc.identifierJ. Math. Phys., 2005, V.46, 043502 (22 pages)
dc.identifierdoi:10.1063/1.1865813
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57765
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectExactly Solvable and Integrable Systems
dc.subject35K57; 35A30
dc.titleHierarchy of Conservation Laws of Diffusion--Convection Equations
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