Some Results on Stochastic Porous Media Equations

Viorel Barbu; Giuseppe Da Prato; Michael Röckner

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 1, page 1-15
  • ISSN: 0392-4041

Abstract

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Some recent results about nonnegative solutions of stochastic porous media equations in bounded open subsets of 3 are considered. The existence of an invariant measure is proved.

How to cite

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Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. "Some Results on Stochastic Porous Media Equations." Bollettino dell'Unione Matematica Italiana 1.1 (2008): 1-15. <http://eudml.org/doc/290489>.

@article{Barbu2008,
abstract = {Some recent results about nonnegative solutions of stochastic porous media equations in bounded open subsets of $\mathbb\{R\}^3$ are considered. The existence of an invariant measure is proved.},
author = {Barbu, Viorel, Da Prato, Giuseppe, Röckner, Michael},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {1-15},
publisher = {Unione Matematica Italiana},
title = {Some Results on Stochastic Porous Media Equations},
url = {http://eudml.org/doc/290489},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Barbu, Viorel
AU - Da Prato, Giuseppe
AU - Röckner, Michael
TI - Some Results on Stochastic Porous Media Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/2//
PB - Unione Matematica Italiana
VL - 1
IS - 1
SP - 1
EP - 15
AB - Some recent results about nonnegative solutions of stochastic porous media equations in bounded open subsets of $\mathbb{R}^3$ are considered. The existence of an invariant measure is proved.
LA - eng
UR - http://eudml.org/doc/290489
ER -

References

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  1. ARONSON, D. G., The porous medium equation, Lecture Notes Math. Vol. 1224, Springer, Berlin (1986), 1-46. Zbl0626.76097MR877986DOI10.1007/BFb0072687
  2. BARBU, V., Analysis and Control of Infinite Dimensional Systems, Academic Press, 1993. Zbl0776.49005MR1195128
  3. BARBU, V. - DA PRATO, G., The two phase stochastic Stefan problem, Probab. Theory Relat. Fields, 124 (2002), 544-560. Zbl1101.60040MR1942322DOI10.1007/s00440-002-0232-4
  4. BARBU, V. - DA PRATO, G. - RÕCKNER, M., Existence and uniqueness of nonnegative solutions to the stochastic porous media equation, Indiana J. Math. (to appear). MR2400255DOI10.1512/iumj.2008.57.3241
  5. BARBU, V. - DA PRATO, G. - RÕCKNER, M., Existence of strong solutions for stochastic porous media equation under general monotonicity conditions, Preprint n. 5, SNS Pisa, March 2007. MR2510012DOI10.1214/08-AOP408
  6. DA PRATO, G. - RÕCKNER, M. - ROZOVSKII, B. L. - WANG, FENG-YU, Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness and Ergodicity, Comm. Partial Differential Equations, 31, no. 1-3 (2006), 277-291. MR2209754DOI10.1080/03605300500357998
  7. DA PRATO, G. - ZABCZYK, J., Stochastic equations in infinite dimensions, Cambridge University Press, 1992. Zbl0761.60052MR1207136DOI10.1017/CBO9780511666223
  8. KRYLOV, N. V. - ROZOVSKII, B. L., Stochastic evolution equations, Translated from Itogi Naukii Tekhniki, Seriya Sovremennye Problemy Matematiki, 14 (1979), 71-146, Plenum Publishing Corp.1981. 
  9. PREVOT, C. - RÕCKNER, M., A concise course on stochastic partial differential equations, Monograph 2006, to appear in Lecture Notes in Mathematics, Springer. MR2329435
  10. REN, J. - RÕCKNER, M. - WANG, FENG-YU, Stochastic generalized porous media and fast diffusions equations, BiBoS-preprint 2006, to appear in J. Diff. Eqn. MR2334594DOI10.1016/j.jde.2007.03.027

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