November 2021 Porous media equations with multiplicative space–time white noise
K. Dareiotis, M. Gerencsér, B. Gess
Author Affiliations +
Ann. Inst. H. Poincaré Probab. Statist. 57(4): 2354-2371 (November 2021). DOI: 10.1214/20-AIHP1139


The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space–time white noise is established in spatial dimension one. The Stroock–Varopoulos inequality is identified as a key tool in the derivation of the corresponding estimates.

L’existence d’une solution martingale pour l’équation stochastique des milieux poreux, dirigée par un bruit non-linéaire multiplicatif en espace et en temps, est établie dans le cas spatial unidimensionnel. L’inégalité de Stroock–Varopoulos est identifiée comme un outil clé dans l’obtention des estimées correspondantes.


BG acknowledges financial support by the DFG through the CRC 1283 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications”. MG thanks the support of the Austrian Science Fund (FWF) through the Lise Meitner programme M2250-N32. The authors thank the anonymous referee for their numerous suggestions on improving the presentation of the paper.


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K. Dareiotis. M. Gerencsér. B. Gess. "Porous media equations with multiplicative space–time white noise." Ann. Inst. H. Poincaré Probab. Statist. 57 (4) 2354 - 2371, November 2021.


Received: 8 April 2020; Revised: 27 October 2020; Accepted: 8 December 2020; Published: November 2021
First available in Project Euclid: 20 October 2021

MathSciNet: MR4330847
zbMATH: 07481288
Digital Object Identifier: 10.1214/20-AIHP1139

Primary: 60H15
Secondary: 35K59 , 35K65

Keywords: porous media equations , stochastic PDEs

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré


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Vol.57 • No. 4 • November 2021
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