# American Institute of Mathematical Sciences

June  2020, 9(2): 375-398. doi: 10.3934/eect.2020010

## Stochastic porous media equations with divergence Itô noise

 Normandie University, INSA de Rouen Normandie, LMI, 7600 Rouen, France

* Corresponding author: ioana.ciotir@insa-rouen.fr

Received  January 2019 Published  June 2020 Early access  August 2019

Fund Project: The author is partially supported by the European Union with the European regional development fund (ERDF, HN0002137) and by the Normandie Regional Council (via the M2NUM and M2SiNum projects) and by the ANR Project QUTE-HPC Quantum Turbulence Exploration by High-Performance Computing (ANR-18-CE46-0013)

We study the existence and uniqueness of solution to stochastic porous media equations with divergence Itô noise in infinite dimensions. The first result prove existence of a stochastic strong solution and it is essentially based on the non-local character of the noise. The second result proves existence of at least one martingale solution for the critical case corresponding to the Dirac distribution.

Citation: Ioana Ciotir. Stochastic porous media equations with divergence Itô noise. Evolution Equations & Control Theory, 2020, 9 (2) : 375-398. doi: 10.3934/eect.2020010
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