Group classification of heat conductivity equations with a nonlinear source

@article{Zhdanov1999GroupCO,
  title={Group classification of heat conductivity equations with a nonlinear source},
  author={Renat Z. Zhdanov and Victor Lahno},
  journal={Journal of Physics A},
  year={1999},
  volume={32},
  pages={7405-7418}
}
We suggest a systematic procedure for classifying partial differential equations (PDEs) invariant with respect to low-dimensional Lie algebras. This procedure is a proper synthesis of the infinitesimal Lie method, the technique of equivalence transformations and the theory of classification of abstract low-dimensional Lie algebras. As an application, we consider the problem of classifying heat conductivity equations in one variable with nonlinear convection and source terms. We have derived a… 

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