Ut=aUxx+cU

U(x,0)=f(x)

U(0,t)=0

Ux(1,t)=0

(Ut - derivative of U according to t

Uxx - second derivative of U according to x)

Question:

Find the smallest C possible, for which the solution U(x,t) does not increase at t increases, for every f(x).

any help would be appreciated ! I have no idea how to begin..