Do you have any idea?
Suppose $f(s)\in C^1(R)$. Let $u(x,t)\in C^{2,1} (U_T) \cap C(U_T)$ bea solution of the following problem
$u_t- \Delta u = f(u)$ on $U_T$;
$u(x,t)=0$ on the boundary;
$u(x,0)=0$, $x \in U$
Prove $u \ge 0$ if $f(0) \ge 0$. It might be an easy problem but i don't know how to approach it.
Thanks