Hi I'm trying to figure out for which values of $w$ of $u(x,t)$ the absolute value of the supremum of $u(x,t)$ is infinity. The function $u(x,t)$ is the following. According to my calculation is going to be all the $w=n$ =integer except $4$ and $6$.
$$ u(x,t) = \sum_{n=1}^{\infty} \{ \frac{1}{2\pi} [\frac{\sin(wx)}{n^2-w^2}] [ \frac{\sin(xn-6x)}{n-6} - \frac{\sin(xn-4x)}{n-4}-$$ $$ - \frac{\sin(nx-4x)}{n+4} - \frac{\sin(xn+6x)}{n+6} ] \} \sin(nx) $$