Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws
Keyword(s):
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.
2021 ◽
pp. 414-420
1992 ◽
Vol 122
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pp. 353-361
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2018 ◽
Vol 4
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pp. 189-206
Keyword(s):
2009 ◽
Vol 62
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pp. 677-705
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1950 ◽
Vol 46
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pp. 570-580
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1982 ◽
Vol 25
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pp. 291-295
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