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Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws
Benjamin B. Mcmillan University of Adelaide, Adelaide, South Australia
Аннотация:
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.
Ключевые слова:
conservation laws, parabolic symbol PDEs, Monge–Ampère equations, characteristic cohomology of exterior differential systems.
Поступила: 17 марта 2020 г.; в окончательном варианте 27 апреля 2021 г.; опубликована 11 мая 2021 г.
Образец цитирования:
Benjamin B. Mcmillan, “Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws”, SIGMA, 17 (2021), 047, 24 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1730 https://www.mathnet.ru/rus/sigma/v17/p47
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