Solutions and symmetry reductions of the radially symmetric non-Newtonian polytropic filtration equations

Abstract

This paper discusses a class of radially symmetric nonlinear diffusion equations, known as non-Newtonian polytropic filtration equations. It is shown that the equations admit certain types of second-order conditional Lie-Bäcklund symmetries. As a result, exact solutions and symmetry reductions of the resulting equations are obtained. The behavior of extinction and blow-up to many of the solutions are also described.