Conservation Laws of Multidimensional Diffusion-Convection Equations

Details Conservation Laws of Multidimensional Diffusion-Convection Equations Conservation Laws of Multidimensional Diffusion-Convection Equations

2006-04-24

arxiv.org/abs/math-ph/0604057v2

Nonlinear Dynamics, 2007, V.49, 71-81

Physics

Mathematical Physics

13 pages

Scientific paper

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., 2005, V.46, 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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