Some aspects of the Floquet theory for the heat equation in a periodic domain.

We treat the linear heat equation in a periodic waveguide Π ⊂ R d , with a regular enough boundary, by using the Floquet transform methods. Applying the Floquet transform F to the equation yields a heat equation with mixed boundary conditions on the periodic cell ϖ of Π , and we analyse the connection between the solutions of the two problems. The considerations involve a description of the spectral projections onto subspaces H S ⊂ L 2 (Π) corresponding certain spectral components. We also show that the translated Wannier functions form an orthonormal basis in H S . [ABSTRACT FROM AUTHOR]