Existence and asymptotic behaviour of solutions for a multi-dimensional fractional thin-film equation
arxiv(2024)
摘要
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 ℝ^d. 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.
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