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

2024/04/04 by Nicola De Nitti, Stefano Lisini, De Nitti, Nicola +5
Engineering · Mathematics · #Fluid Dynamics and Thin Films #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2404.03633

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 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.

Related

• On a fractional thin film equation
• Classical solvability of the multidimensional free boundary problem for the thin film equation in the case of partial wetting
• Fractional high order thin film equation: gradient flow approach
• Finite and infinite speed of propagation for porous medium equations with nonlocal pressure
• Asymptotic behaviour of a porous medium equation with fractional\n diffusion