Initial layer
= Initial layer
{title2=$\sigma=t/\epsilon$}
An <initial layer> is a short transient needed when the reduced <outer solution> cannot satisfy the original <initial condition>. On an inner time scale, terms multiplied by a small parameter remain comparable to the retained dynamics. For $\epsilon c_t=1-(1+\beta)c$, $c(0)=0$, the inner solution $c=(1-e^{-(1+\beta)t/\epsilon})/(1+\beta)$ matches the outer value $1/(1+\beta)$ while retaining the initial datum.