An exact solution for a nonlinear diffusion equation in a radially symmetric inhomogeneous medium
We present an exact solution for a nonlinear diffusion equation by considering the radially symmetric ? ? -dimensional case in inhomogeneous medium. This exact solution describes the evolution in space and time of an initial distribution of a diffusing substance. The diffusion coefficient is assumed to be dependent on both, positional coordinate (radial distance) and concentration, with power law nonlinearity. The exact solution is novel and it was obtained thanks to general similarity transformation. A constant time is involved in the similarity variable which allows the definition of the initial amount of the diffusant in the system. We provide an exact expression of the front propagation of the diffusing substance. The proposed exact solution is useful for verification of numerical simulation tools as well as for comparison with laboratory experiments.
exact solution nonlinear diffusion inhomogeneous medium similarity solution