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Group classification and analytical solutions of a radially symmetric avascular cancer model

We consider a system of partial differential equations modeling tumors. The system under consideration describes the spatial dynamics of the tumor cells, extracellular matrix, and matrix degrading enzymes. We first carry out a complete group classification of the Lie point symmetries of this model. Next, we use symmetry techniques to construct invariant solutions for it. In addition, we consider a second system of partial differential equations, coupling to the original one the concentration of oxygen, and we find several analytical solutions to this system. Most of the solutions are biologically relevant and consistent with the evolution of such tumors.