You mean like some level of smoothness. For sure. In most cases I would use a separation of variables. For special cases of $f(u)$ - something else.
Thanks for pointing that out!
Yeah, I was more getting at the "separability" of $f$. Characteristics doesn't seem to have that drawback in this case.What I meant to say was the method of characteristics (What was I thinking???) That's what happens when I think mathematics w/o my first cup of tea in the morning.