Existence and asymptotic behaviour of solutions for a multi-dimensional fractional thin-film equation

In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in Rᵈ. The nonlocal operator we consider is the spectral fractional Laplacian with Neumann boundary conditions. In the case of a "strong slippage" regime with "complete wetting" interfacial conditions, we prove local entropy estimates that entail finite speed of propagation of the support and a lower bound for the waiting time phenomenon.