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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
The Schrödinger equation with fluctuating nonlinearity in the energy space
Max Sauerbrey, Joris van Winden
We study nonlinear Schrödinger equations with nonlinear Stratonovich noise \begin{equation*} \mathrm{d} u\,=\, i\bigl[ Δu \,+\, λ|u|^{p-1}u\bigr] \, \mathrm{d} t \,+\,i|u|^{(q-1)/2…
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…