WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
The Self-Similar Solutions of a Diffusion Equation
Author:
Abstract: This paper discusses the diffusion equation with a damping term as follows
$$ut = div (|Du^{m}|^{p−2}Du^{m})-u^{q1}|Du^{m}|p^{1}$$,
where p > 2, m > 1, and p > p1, q1 +p1m > m(p−1) > 1. By the standard Picard iteration method, a sufficient condition is given to the existence of the singular self-similar solutions. Moreover, the paper gives a classification for these singular self-similar solutions.