Geodesic
Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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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, characteristic cohomology of exterior differential systems.
Mots-clés : parabolic symbol PDEs, Monge–Ampère equations 
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     author = {Benjamin B. Mcmillan},
     title = {Geometry and {Conservation} {Laws} for a {Class} of {Second-Order} {Parabolic} {Equations} {II:} {Conservation} {Laws}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2021},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a46/}
}
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Benjamin B. Mcmillan. Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a46/

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