Localization of solutions to stochastic porous media equations: finite speed of propagation

Viorel Barbu (Al.I.Cuza University)
Michael Roeckner (Bielefeld University)

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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Pages: 1-11

Publication Date: January 29, 2012

DOI: 10.1214/EJP.v17-1768

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