Eventual self-similarity of solutions for the diffusion equation with nonlinear absorption and a point source

This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point source. In one space dimension, solutions of these problems with zero initial data are known to approach the stationary solution in an asymptotically self-similar manner. Here we show that this conclusion remains...