A class of similar solutions of the non-linear diffusion equation

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Abstract
The existence of a general class of similar solutions of the diffusion equation is demonstrated, when the boundary conditions vary as a simple power of time, and the transport coefficient varies non-linearly as a power of the concentration. Although earlier workers have described specific exact solutions, which are members of this class, the class as a whole has not previously been investigated. A simple method is given for the numerical integration of the characteristic differential equation of the profile for the case when an exact solution is not available. The use of these solutions in studies of laser interaction with solid targets, and as test problems for thermal conduction routines, is briefly discussed.