Stochastic porous media equations with divergence Itô noise

Ioana Ciotir (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

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.

Mots clés: Stochastic PDE's; porous media operator; divergence noise

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Ioana Ciotir. Stochastic porous media equations with divergence Itô noise. Evolution Equations and Control Theory, 2020, 9 (2), pp.375-398. ⟨10.3934/eect.2020010⟩. ⟨hal-02889493⟩