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arXiv · 2404.03633

Existence and finite speed of propagation of solutions for a multi-dimensional fractional thin-film equation

Nicola De Nitti·Stefano Lisini·Antonio Segatti·Roman Taranets
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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 $\mathbb{R}^d$. 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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Nicola De Nitti, Stefano Lisini, Antonio Segatti, Roman Taranets. 2024-04-04. Existence and finite speed of propagation of solutions for a multi-dimensional fractional thin-film equation. https://arxiv.org/abs/2404.03633

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