Hello all,

I'm working on a problem, that at the first step requires a growth estimate, that I can't seem to get. Here's the pertinent information:

Let $\displaystyle u\in C^2(\mathbb{R})$ satisfying

$\displaystyle \lim_{|x|+|t|\to\infty}\frac{u(x,t)}{|x|^5+|t|^5}= 0.$

Show that there exists $\displaystyle C>0$ so that

$\displaystyle |u(x,t)|\leq C(1+|x|+|t|)^5$

for all $\displaystyle x,t\in\mathbb{R}$.

Thanks for the help!