Existence and finite speed of propagation of solutions for a multi-dimensional fractional thin-film equation
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916743217152000 |
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| author | De Nitti, Nicola Lisini, Stefano Segatti, Antonio Taranets, Roman |
| author_facet | De Nitti, Nicola Lisini, Stefano Segatti, Antonio Taranets, Roman |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_03633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and finite speed of propagation of solutions for a multi-dimensional fractional thin-film equation De Nitti, Nicola Lisini, Stefano Segatti, Antonio Taranets, Roman Analysis of PDEs 35R11, 35R09, 26A33 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. |
| title | Existence and finite speed of propagation of solutions for a multi-dimensional fractional thin-film equation |
| topic | Analysis of PDEs 35R11, 35R09, 26A33 |
| url | https://arxiv.org/abs/2404.03633 |