Givevn the following PDE
$u_{tt}=u_{rr}+\frac{2}{r}u_r$
$u(r,0)=1 $if $r\leq1$ else 0
$u_t(r,0)=0$
find $u(0,t)$
my attempt:
we know from delamber formula that $u(r,t)=\frac{1}{2r}[(r+t)f(r+t)+(r-t)f(r-t)]$
where is mirroring $u(r,0)$ for even function so $f(r+t)=1$ if $-1\leq r+t\leq1$ else $0$
and the same for $f(r-t)$ but I didn't figure out how to continue from here to calculate the lim of $r\to0$