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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

Robert Lewis
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user216045
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    For some basic information about writing math at this site see e.g. here, here, here and here. –  Feb 17 '15 at 04:51
  • Looks like you need to generalize the maximum principle for this. –  Feb 17 '15 at 05:02
  • I tried to $\LaTeX$ify your math; the problem seems interesting enough to motivate me to do so. I hope the results are in keeping with your intended question; if not, feel free to change it, of course, although you might want to remember to enclose your $\LaTeX$ in $$ signs. You might also want to consider explicitly defining $U$, $U_T$ etc. Cheers! – Robert Lewis Feb 17 '15 at 05:19

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