Local uniform convergence and eventual positivity of solutions to biharmonic heat equations

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