Work

Parabolic-hyperbolic splitting in support propagation for stochastic porous media equations

Year: 2026

Type: preprint

Abstract: 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 in previous works, where energies are localized by weighting them with a spatial bump function, we weight them with profiles which are solutions to stochastic transport equations. This modulates out the support propagation due to the conservative noise term, and energy arguments---which otherwise fail in this setting---are again applicable. As a result, finite speed of propagation along with sufficient and necessary conditions on the existence of waiting time phenomena (modulo stochastic transport) are proven. These methods and results demonstrate, on short time scales, that the support propagation may be disintegrated into two independent parts, one due to the evolution of the porous media equation and one due to stochastic transport.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11468

Authors: Sauerbrey, Max, Utley, Joshua

Institutions: Max Planck Institute for Mathematics in the Sciences, Friedrich-Alexander-Universität Erlangen-Nürnberg

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Award: GRK 2339: IntComSin: Grenzflächen, komplexe Strukturen und singuläre Grenzwerte in der Kontinuumsmechanik Analysis und Numerik

OpenAlex ID: W7212270057

Cites: 6

Cited by:

Related to: 10