  The well known nonlinear model for describing the solid tumour growth [Byrne
HM., et al. Appl Math Letters 2003;16:567-74] is under study using an approach
based on Lie symmetries. It is shown that the model in the two-dimensional (in
space) approximation forms a (1+2)-dimensional boundary value problem, which
admits a highly nontrivial Lie symmetry. The special case involving the
power-law nonlinearities is examined in details. The symmetries derived are
applied for the reduction of the nonlinear boundary value problem in question
to problems of lower dimensionality. Finally, the reduced problems with
correctly-specified coefficients were exactly solved and the exact solutions
derived were analysed, in particular, some plots were build in order to
understand the time-space behaviour of these solutions and to discuss their
biological interpretation.
