 Solution

With the travelling wave coordinate $\xi =x-ct$, the reaction-diffusion system becomesAt the advancing leading edge the healthy-tissue density is small. Put $f(\xi )\sim e^{-\lambda \xi }$ with $\lambda >0$. The linearization at $f=0$ givesso a nonoscillatory decaying front requires real positive roots,The pulled travelling front selects the Fisher-KPP minimum wave speed, and therefore

For the initial wound $0<x<W$, two mirror-image fronts enter from its endpoints. The left front moves right from $x=0$ and the right front moves left from $x=W$, each with speed approximately $c_{\min }$. A sequence of sketches would show the initial rectangular depression becoming two smooth monotone transition layers, the zero-density plateau shrinking, and the two layers meeting near $x=W/2$ before the profile relaxes to $S=1$. Their meeting time isThere is an additional local relaxation time of order $1/r$ if “close to one” is assigned a fixed numerical tolerance, so the displayed estimate is the dominant healing time when $W$ is large compared with the front width $\sqrt{D/r}$.