INTERFACE PROPAGATION PROPERTIES FOR A NONLOCAL THIN-FILM EQUATION

De Nitti N, Taranets RM (2024)

Publication Type: Journal article

Publication year: 2024

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 56

Pages Range: 173-196

Journal Issue: 1

DOI: 10.1137/22M1510297

Abstract

We consider a degenerate nonlocal parabolic equation in a one-dimensional domain introduced to model hydraulic fractures. The nonlocal operator is given by a fractional power of the Laplacian and the degenerate mobility exponent corresponds to a ``strong slippage" regime with ``complete wetting" interfacial conditions for local thin-film equations. Using a localized entropy estimate and a Stampacchia-type lemma, we establish a finite speed of propagation result and sufficient conditions (and lower bounds) for the waiting-time phenomenon.

Authors with CRIS profile

Nicola De Nitti Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Institute for Applied Problems of Mechanics and Mathematics (IAPMM) / Інститут прикладних проблем механіки і математики UA Ukraine (UA)

How to cite

APA:

De Nitti, N., & Taranets, R.M. (2024). INTERFACE PROPAGATION PROPERTIES FOR A NONLOCAL THIN-FILM EQUATION. SIAM Journal on Mathematical Analysis, 56(1), 173-196. https://dx.doi.org/10.1137/22M1510297

MLA:

De Nitti, Nicola, and Roman M. Taranets. "INTERFACE PROPAGATION PROPERTIES FOR A NONLOCAL THIN-FILM EQUATION." SIAM Journal on Mathematical Analysis 56.1 (2024): 173-196.

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