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References
- V. Barbu, G. Da Prato. Ergodicity for nonlinear stochastic equations in variational formulation. Appl. Math. Optim. 53 (2006), no. 2, 121--139. MR2172782 (2007d:60030)
- V. Barbu, G. Da Prato. Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation. Stochastic Process. Appl. 120 (2010), no. 7, 1247--1266. MR2639746 (2011g:60105)
- V. Barbu, G. Da Prato, M. Röckner. Stochastic porous media equations and self-organized criticality. Comm. Math. Phys. 285 (2009), no. 3, 901--923. MR2470909 (2011b:35580)
- J. G. Berryman, C. J. Holland. Stability of the separable solution for fast diffusion. Arch. Rational Mech. Anal. 74 (1980), no. 4, 379--388. MR0588035 (81m:35065)
- V. I. Bogachev, G. Da Prato, M. Röckner. Invariant measures of generalized stochastic equations of porous media. (Russian) Dokl. Akad. Nauk 396 (2004), no. 1, 7--11. MR2115900 (2005k:60191)
- I. Ciotir, J. M. Tölle. Convergence of solutions to the stochastic $p$-Laplace equations as $p$ goes to $1$, Preprint, (2010), BiBoS-Preprint 11-01-371
- G. Da Prato, M. Röckner, B. L. Rozovskiĭ, F.-Y. Wang. Strong solutions of stochastic generalized porous media equations: existence, uniqueness, and ergodicity. Comm. Partial Differential Equations 31 (2006), no. 1-3, 277--291. MR2209754 (2007b:60153)
- G. Da Prato, J. Zabczyk. Ergodicity for infinite-dimensional systems. London Mathematical Society Lecture Note Series, 229. Cambridge University Press, Cambridge, 1996. xii+339 pp. ISBN: 0-521-57900-7 MR1417491 (97k:60165)
- E. DiBenedetto. Degenerate parabolic equations. Universitext. Springer-Verlag, New York, 1993. xvi+387 pp. ISBN: 0-387-94020-0 MR1230384 (94h:35130)
- A. Es-Sarhir, M.-K. von Renesse. Ergodicity of stochastic curve shortening flow in the plane. Preprint, to appear in SIAM J. Math. Anal. (2010), arXiv:1003.2074
- A. Es-Sarhir, M.-K. von Renesse, W. Stannat. Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow. Preprint (2010), arXiv:1008.1961
- B. Gess, W. Liu, M. Röckner. Random attractors for a class of stochastic partial differential equations driven by general additive noise. J. Diff. Equations 251 (2011), no. 4--5, 1225--1253.
- N. V. Krylov, B. L. Rozovskiĭ. Stochastic evolution equations. (Russian) Current problems in mathematics, Vol. 14 (Russian), pp. 71--147, 256, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1979. MR0570795 (81m:60116)
- W. Liu. Harnack inequality and applications for stochastic evolution equations with monotone drifts. J. Evol. Equ. 9 (2009), no. 4, 747--770. MR2563674 (2011d:60201)
- W. Liu. On the stochastic $p$-Laplace equation. J. Math. Anal. Appl. 360 (2009), no. 2, 737--751. MR2561270 (2010j:35633)
- W. Liu. Large deviations for stochastic evolution equations with small multiplicative noise.. Appl. Math. Optim. 61 (2010), no. 1, 27--56. MR2575313 (2011d:60081)
- W. Liu, M. Röckner. SPDE in Hilbert space with locally monotone coefficients. J. Funct. Anal. 259 (2010), no. 11, 2902--2922. MR2719279
- W. Liu, F.-Y. Wang. Harnack inequality and strong Feller property for stochastic fast-diffusion equations. J. Math. Anal. Appl. 342 (2008), no. 1, 651--662. MR2440828 (2009k:60137)
- É. Pardoux. Équations aux dérivées partielles stochastiques de type monotone. (French) Séminaire sur les Équations aux Dérivées Partielles (1974–1975), III, Exp. No. 2, 10 pp. Collège de France, Paris, 1975. MR0651582 (58 #31406)
- C. Prévôt, M. Röckner. A concise course on stochastic partial differential equations. Lecture Notes in Mathematics, 1905. Springer, Berlin, 2007. vi+144 pp. ISBN: 978-3-540-70780-6; 3-540-70780-8 MR2329435 (2009a:60069)
- Ph. Rosenan. Fast and super fast diffusion processes. Phys. Rev. Lett. 74 (1995), no. 11, 7--14.
- F.-Y. Wang. Harnack inequality and applications for stochastic generalized porous media equations. Ann. Probab. 35 (2007), no. 4, 1333--1350. MR2330974 (2008e:60192)
- X. Zhang. On stochastic evolution equations with non-Lipschitz coefficients. Stoch. Dyn. 9 (2009), no. 4, 549--595. MR2589037 (2011d:60196)

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