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.
Existence and finite speed of propagation of solutions for a multidimensional fractional thin-film equation
Lisini, Stefano;Segatti, Antonio;
2026-01-01
Abstract
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.File in questo prodotto:
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