Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws
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Published:2021-05-11
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Volume:
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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language:
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Short-container-title:SIGMA
Author:
McMillan Benjamin B.,
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
Geometry and Topology,Mathematical Physics,Analysis