Ken Sekimoto, Takahiko Fujita
Published 2012-10-31, updated 2017-11-19Version 2
The aim of the this rather technical note is to summarize the properties and utilities of the family of self-similar solutions of the diffusion equation in 1D and the similar parabolic partial-differential equations. In the first part we analyze the family of self-similar solutions focusing on the relationship among them. In the second part we describe the utility of the "exotic" self-similar solutions that decay or grow algebraically for large argument of the scaling variable.
Comments: 7 pages, 7 figures, 2nd version, unpublished
On a diffusion equation with rupture
On some properties of travelling water waves with vorticity
Eventual self-similarity of solutions for the diffusion equation with nonlinear absorption and a point source
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