Heat transfer at nanoscale and boundary conditions

A model of nonlocal heat transfer at nanoscale in rigid bodies is considered. Depending on the relevance of the particular interaction’s mechanism between the heat carriers and the lateral walls, three different strategies for the setting-up of the boundary conditions are analyzed, and the consequent forms of the basic fields have been obtained, as well. From the physical point of view, the possible influence of those interactions on the unknown fields is pointed out. From the mathematical point of view, instead, the well-posedness of the problem is shown.