  We study the evolution equation associated with the biharmonic operator on
infinite cylinders with bounded smooth cross-section subject to Dirichlet
boundary conditions. The focus is on the asymptotic behaviour and positivity
properties of the solutions for large times. In particular, we derive the local
eventual positivity of solutions. We furthermore prove the local eventual
positivity of solutions to the biharmonic heat equation and its generalisations
on Euclidean space. The main tools in our analysis are the Fourier transform
and spectral methods.
