# 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…

## 56 Citations

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