3 papers
math.AP2026
Free Boundary Propagation of a Thin-Film Equation with Nonlinear Diffusion: Scale-Consistent Methods for Optimal Results
Joshua Utley
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…
math.AP2026
Parabolic-hyperbolic splitting in support propagation for stochastic porous media equations
Max Sauerbrey, Joshua Utley
We develop a randomly-localized energy method to derive qualitative results on the support propagation of stochastic porous media equations with linear conservative noise. Unlike i…
math.AP2026
Finite speed of propagation and waiting time phenomena for stochastic porous media equations with nonlinear conservative noise
Günther Grün, Max Sauerbrey, Joshua Utley
Starting from localized energy estimates, we prove finite speed of propagation for kinetic solutions to stochastic porous media equations with nonlinear conservative noise, the exi…