I have been searching in some literature and Wikipedia about the definition or explanation of outer region, outer solution, inner region and inner solution of boundary layer theory, perturbation theory and asymptotic matching. But I could not find any useful and easily understood one.
In Wikipedia, it is written An approximation in the form of an asymptotic series is obtained in the transition layer(s) by treating that part of the domain as a separate perturbation problem. This approximation is called the "inner solution," and the other is the "outer solution"
I don't find this explanation clear enough. I am a bit confused what exactly is outer/inner region and outer/inner solution? Is it correct if I interpret outer and inner as outside the boundary and inside the boundary? But again, a question arises, where is considered as outside/inside? Does it have any relationship with the order of $\epsilon$, that is $O(\epsilon)$? Such as the limit as $\epsilon\to0$ or something like that?
I would just want some easily understood and not so deep explanation since I am quite immature in this field. I apologise for such a naive question, this idea has always been so vague to me, I just want to get a better understanding. I will really appreciate if anyone would like to provide some explanations and share some insights.