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Type: Journal article
Title: Geometry and conservation laws for a class of second-order parabolic equations ii: conservation laws
Author: McMillan, B.B.
Citation: Symmetry, Integrability and Geometry: Methods and Applications, 2021; 17:1-24
Publisher: Institute of Mathematics NAS of Ukraine
Issue Date: 2021
ISSN: 1815-0659
Statement of
Benjamin B. McMillan
Abstract: I 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.
Keywords: Conservation laws; parabolic symbol PDEs; Monge{Ampere equations; characteristic cohomology of exterior di erential systems
Rights: Copyright status unknown
DOI: 10.3842/SIGMA.2021.047
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