First-Order Sign-Invariants and Exact Solutions of the Radially Symmetric Nonlinear Diffusion Equations with Gradient-Dependent Diffusivities

Abstract

The sign-invariant theory is used to study the radially symmetric nonlinear diffusion equations with gradient-dependent diffusivities. The first-order non-stationary sign-invariants and the first-order non-autonomous sign-invariants admitted by the governing equations are identified. As a consequence, the exact solutions to the resulting equations are constructed due to the corresponding reductions. The phenomena of blow-up, extinction and behavior of some solutions are also described.