Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws
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 satisfi...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211302 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws. Benjamin B. McMillan. SIGMA 17 (2021), 047, 24 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
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| ISSN: | 1815-0659 |