Local uniform convergence and eventual positivity of solutions to biharmonic heat equations. (Q6133015)

This article is concerned with the heat equation for the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The authors discuss the asymptotic behavior and positivity properties of the solutions for large times. It is shown the local eventual positivity of solutions to the biharmonic heat equation and its generalizations on Euclidean space. The main tools of the approach are the Fourier transform combined with spectral methods.