Conservations laws for a porous medium equation through nonclassical generators |
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Institution: | 1. Institute of Mathematics, Ukrainian National Academy of Sciences, 3 Tereshchenkivs’ka Street, Kyiv 01601, Ukraine;2. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK |
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Abstract: | In Ibragimov (2007) 13] a general theorem on conservation laws was proved. In Gandarias (2011) and Ibragimov (2011) 7], 15] the concepts of self-adjoint and quasi self-adjoint equations were generalized and the definitions of weak self-adjoint equations and nonlinearly self-adjoint equations were introduced. In this paper, we find the subclasses of nonlinearly self-adjoint porous medium equations. By using the property of nonlinear self-adjointness, we construct some conservation laws associated with classical and nonclassical generators of the differential equation. |
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Keywords: | Self-adjointness Quasi self-adjointness Weak self-adjointness Nonlinear self-adjointness Symmetries Partial differential equations Conservation laws |
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