Quote by Dick
I think you are right. It should be u_yy, the second derivative. Not (u_y)^2. It's a linear operator. Is it a typo?

But if that is the case, why don't they write ∂
_{yy} (instead of (∂
_{y})
^{2}? (I am not sure whether it's a typo, but it seems to me that the context of it highly suggests it isn't)
Also, if they really meant (u
_{y})
^{2}, how could it be expressed as an "operator"?
Thanks!