Consider a flux-limited diffusion process, where ut=[G(ux)]x with G(∞)<∞ and G′(s)≥0. We show that if the pr ofile u(0, x initially has a sharp front, then the sharp front may not be resolved immediately. Instead, the front may remain perfectly sharp for a finite time, during which the height of the jump decays to zero. In this case the profile near the sharp front takes a self-similar form u= tf(x/ t), with the front remaining sharp for a time [h/2f(0)]2, where h is the height of the initial discontinuity . We also determine when an initially sharp jump will remain sharp for a finite time, and when it will be resolved immediately.
|Number of pages||5|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - 27 Nov 1989|