We study the asymptotic behavior of solutions for three types
of nonlinear evolution equations. Parabolic, hyperbolic as well
as elliptic equations on the cylinder $\Omega\times (0,\infty)$
are considered, where $\Omega$ is a ball in $R^N$, $N>1$.

Under appropriate conditions, we establish the existence of
an asymptotic profile of the solution as the unbounded variable
tends to infinity.