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

   
@article{EJP1768,
	author = {Viorel Barbu and Michael Roeckner},
	title = {Localization of solutions to stochastic porous media equations:  finite speed of propagation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Wiener process; porous media equation; energy method; stochastic flow},
	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 $(0,t({\omega}))$.
},
	pages = {no. 10, 1-11},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1768},    
        url = {http://ejp.ejpecp.org/article/view/1768}}