Plug in u = 0. The result C > 0 pops right out.
I am trying to understand the proof to Gronwall's Inequality, but I have one major issue I was hoping someone could get me through. My issue actually makes the proof incorrect.
First, the statement of Gronwall's Inequality
Let
be continuous functions and let be a constant. Then if
For , it follows that
for .
Proof:
How do we know ?
How do we know ?
EDIT: I guess both my questions boil down to how do we know ? Since, we know by
EDIT2: . However, I still don't see how we know .