Calculus of Variations and Geometric Measure Theory

N. De Nitti - R. Taranets

Interface propagation properties for a fractional thin-film equation

created by denitti on 11 Jan 2023


Submitted Paper

Inserted: 11 jan 2023

Year: 2022


We consider a degenerate nonlocal parabolic equation introduced to model hydraulic fractures, where the nonlocal operator is given by a fractional power of the Laplacian. 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.