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2012 Localization of solutions to stochastic porous media equations: finite speed of propagation
Viorel Barbu, Michael Roeckner
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Electron. J. Probab. 17: 1-11 (2012). DOI: 10.1214/EJP.v17-1768

Abstract

It is proved that the solutions to the slow diffusion stochastic porous media equation $dX-{\Delta}( |X|^{m-1}X )dt=\sigma(X)dW_t,$ $ 1< m\le 5,$ in $\mathcal{O}\subset\mathbb{R}^d,\ d=1,2,3,$ have the property of finite speed of propagation of disturbances for $\mathbb{P}\text{-a.s.}$ ${\omega}\in{\Omega}$ on a sufficiently small time interval $(0,t({\omega}))$.

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Viorel Barbu. Michael Roeckner. "Localization of solutions to stochastic porous media equations: finite speed of propagation." Electron. J. Probab. 17 1 - 11, 2012. https://doi.org/10.1214/EJP.v17-1768

Information

Accepted: 29 January 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1246.60085
MathSciNet: MR2878789
Digital Object Identifier: 10.1214/EJP.v17-1768

Subjects:
Primary: 60H15
Secondary: 35R60

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