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.
Interface propagation properties for a nonlocal thin-film equation
De Nitti N
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2024-01-01
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.File in questo prodotto:
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