Some recent results about nonnegative solutions of stochastic porous media equations in bounded open subsets of are considered. The existence of an invariant measure is proved.
@article{BUMI_2008_9_1_1_1_0, author = {Viorel Barbu and Giuseppe Da Prato and Michael R\"ockner}, title = {Some Results on Stochastic Porous Media Equations}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {1}, year = {2008}, pages = {1-15}, zbl = {1205.60109}, mrnumber = {2387994}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_1_1_0} }
Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael. Some Results on Stochastic Porous Media Equations. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 1-15. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_1_1_0/
[1] 1224, Springer, Berlin (1986), 1-46. | MR 877986 | Zbl 0626.76097
, The porous medium equation, Lecture Notes Math. Vol.[2] | MR 1195128 | Zbl 0776.49005
, Analysis and Control of Infinite Dimensional Systems, Academic Press, 1993.[3] The two phase stochastic Stefan problem, Probab. Theory Relat. Fields, 124 (2002), 544-560. | MR 1942322 | Zbl 1101.60040
- ,[4] Existence and uniqueness of nonnegative solutions to the stochastic porous media equation, Indiana J. Math. (to appear). | MR 2400255
- - ,[5] Existence of strong solutions for stochastic porous media equation under general monotonicity conditions, Preprint n. 5, SNS Pisa, March 2007. | MR 2510012
- - ,[6] Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness and Ergodicity, Comm. Partial Differential Equations, 31, no. 1-3 (2006), 277-291. | MR 2209754
- - - ,[7] | MR 1207136 | Zbl 0761.60052
- , Stochastic equations in infinite dimensions, Cambridge University Press, 1992.[8] 14 (1979), 71-146, Plenum Publishing Corp. 1981.
- , Stochastic evolution equations, Translated from Itogi Naukii Tekhniki, Seriya Sovremennye Problemy Matematiki,[9] | MR 2329435
- , A concise course on stochastic partial differential equations, Monograph 2006, to appear in Lecture Notes in Mathematics, Springer.[10] Stochastic generalized porous media and fast diffusions equations, BiBoS-preprint 2006, to appear in J. Diff. Eqn. | MR 2334594
- - ,