Group classification of a class of systems of nonlinear diffusion equations. I
DOI:
https://doi.org/10.3842/umzh.v78i3-4.8902Keywords:
Group classification,, system of diffusion equations,, Lie symmetries,, equivalence group,, (1 1)-dimensional nonlinear evolution equationsAbstract
UDC 517.95:512.81
We study the Lie symmetries of a class of systems of $(1+1)$-dimensional nonlinear diffusion equations. The equivalence algebra and the kernel of maximal invariance algebras of this class are found. We prove that there are nine inequivalent subclasses of this class for which the corresponding diffusion systems admit Lie symmetry extensions. We also perform the exhaustive group classification of the systems of nonlinear diffusion equations that belong to the first identified subclass.
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