Nonlinear self-adjointness of a 2D generalized second order evolution equation |
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Authors: | Yuri Bozhkov,Kê nio A.A. Silva |
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Affiliation: | Instituto de Matemática, Estatística e Computação Científica - IMECC, Universidade Estadual de Campinas - UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859 - Campinas - SP, Brazil |
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Abstract: | We study the nonlinear self-adjointness of a general class of quasilinear 2D second order evolution equations which do not possess variational structure. For this purpose, we use the method of Ibragimov, devised and developed recently. This approach enables one to establish the conservation laws for any differential equation. We first obtain conditions determining the self-adjoint sub-class in the general case. Then, we establish the conservation laws for important particular cases: the Ricci Flow equation, the modified Ricci Flow equation and the nonlinear heat equation. |
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Keywords: | 35J50 35J20 35J60 |
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