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Conservation laws of multidimensional diffusion--convection equations

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Abstract

All possible linearly independent local conservation laws for n-dimensional diffusion–convection equations u t=(A(u)) ii +(B i(u)) i were constructed using the direct method and the composite variational principle. Application of the method of classification of conservation laws with respect to the group of point transformations [R.O.~Popovych, N.M. Ivanova, J. Math. Phys. 46, 2005, 043502 (math-ph/0407008)] allows us to formulate the result in explicit closed form. Action of the symmetry groups on the conservation laws of diffusion equations is investigated and generating sets of conservation laws are constructed.

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Authors and Affiliations

  1. Institute of Mathematics of National Academy of Sciences of Ukraine, 3, Tereshchenkivska Str., Kyiv-4, 01601, Ukraine

    Nataliya M. Ivanova

  2. Department of Mathematics, UBC, Vancouver, BC, Canada, V6T 1Z2

    Nataliya M. Ivanova

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  1. Nataliya M. Ivanova
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Correspondence to Nataliya M. Ivanova.

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Ivanova, N.M. Conservation laws of multidimensional diffusion--convection equations. Nonlinear Dyn 49, 71–81 (2007). https://doi.org/10.1007/s11071-006-9104-2

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  • DOI: https://doi.org/10.1007/s11071-006-9104-2

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