Interface propagation properties for a nonlocal thin-film equation
SIAM JOURNAL ON MATHEMATICAL ANALYSIS(2024)
摘要
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.
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关键词
spectral fractional Laplacian,hydraulic fractures,nonlocal thin-film equation,higher order degenerate parabolic equations
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