The diffraction of a diffusion front by concave and convex wedges is studie
d for Nagumo and Fisher's equations on the limit of fast reaction and small
diffusion, using both the asymptotic theory and full numerical solutions.
For the case of a convex corner, the full numerical solution confirms that
the front evolves according to the asymptotic theories. On the other hand,
for the concave corner, it is shown numerically that the diffraction produc
es at the corner a region of low values of the solution for both the Nagumo
and Fisher's equations. Moreover, in both cases, the front eventually evol
ves, leaving behind a cavity. In the case of the Nagumo equation, it is sho
wn that the long-term behavior of the diffraction front is just a traveling
front, bent at the sloping wall. The bent region maintains its size as the
front travels. This behavior is predicted by an exact traveling wave solut
ion of the asymptotic equation for the front propagation. Good agreement is
found between the numerical and the asymptotic solutions. On the other han
d, behavior of the diffracted front for Fisher's equation is different. In
this case, the front is bent at the sloping wall, but, as time passes, the
bend becomes smaller and moves toward the sloping wall. This behavior is, a
gain, predicted by the asymptotic solution. The numerics strongly suggest t
hat the final state for the concave corner is a steady cavity-like solution
with low values at the corner and high values away from it. This solution
has an angular dependence that varies with the angle of the sloping wall.