I have troubles understanding the proof of the connection between BBM and KPP equation. I mean the proof of the next lemma from the lecture notes of Anton Bovier about BBM, link. This is almost whole proof, on the next page only the formula (3.10) is repeated.
My problem is, I do not see how to get equation (3.10) from (3.11). I did some computations, to no avail. I have checked the original work of McKean ([44]), but there explanation is even more concise.