Abstract
The present paper analysed the model of a pre-cancerous cell population which describes early carcinogenesis from the view point of invariant solutions associated with conservation laws. The conservation laws related with symmetries of the nonlinear heat equations are obtained and used for constructing analytic solutions. The determination of conservation laws is obtained by mean of Noether’s theorem. This result is used to construct a linear Lagrangian of the given pre-cancerous model. The reduction of a three- dimensional system into a corresponding one dimensional system serves to obtained a nonlinear Lagrangian. L’application of Lie group theory to a reduced model produces the combinations of parameters in which the linearization of the system is established and provide the corresponding analytical solutions.
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