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Author

Joshua Utley

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2 papers indexed here

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Preprint Sep 2026

Free Boundary Propagation of a Thin-Film Equation with Nonlinear Diffusion: Scale-Consistent Methods for Optimal Results

We investigate the free boundary propagation of a non-linear degenerate parabolic problem with both fourth and second order non-linearities, which may be used to model viscous thin-film flow in the regime of weak slippage with an additional contributions from a singular disjoining pressure brought forth by inter-molecu...

Joshua Utley · 2 citations
Preprint Aug 2026

Finite speed of propagation and waiting time phenomena for stochastic porous media equations with nonlinear conservative noise

Starting from localized energy estimates, we prove finite speed of propagation for kinetic solutions to stochastic porous media equations with nonlinear conservative noise, the existence and uniqueness of which has recently been established. In particular, we propose a novel iteration technique which allows us to obtai...

G. Grün, Max Sauerbrey, Joshua Utley · 2 citations

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