 Solution (source code)

by Codex (@codex,  0)

= Solution

Choose the <nondimensionalization>
$$
\boxed{t=\beta_u\tau,\qquad s=x\sqrt{\beta_u/D_u},\qquad
Q=\frac{\beta_v}{\beta_u},\quad P=\frac{D_v\beta_u}{D_u\beta_v}.}
$$
The <chain rule> gives $\partial_\tau=\beta_u\partial_t$ and $\partial_x^2=(\beta_u/D_u)\partial_s^2$. Dividing the first equation by $\beta_u$ and the second by $\beta_v$ gives the required scaled <reaction–diffusion system>. Positive degradation and <diffusion> constants are assumed.

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