The Global Random Attractor for a Class of Stochastic Porous Media Equations

Beyn W-J, Gess B, Lescot P, Röckner M (2011)
Communications in Partial Differential Equations 36(3): 446-469.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We prove new L2-estimates and regularity results for generalized porous media equations oshifted byo a function-valued Wiener path. To include Wiener paths with merely first spatial (weak) derivates we introduce the notion of o-monotonicityo for the non-linear function in the equation. As a consequence we prove that stochastic porous media equations have global random attractors. In addition, we show that (in particular for the classical stochastic porous media equation) this attractor consists of a random point.
Stichworte
differential equations; Stochastic partial; Random attractor; Random dynamical systems; Stochastic porous medium equation
Erscheinungsjahr
2011
Zeitschriftentitel
Communications in Partial Differential Equations
Band
36
Ausgabe
3
Seite(n)
446-469
ISSN
0360-5302
Page URI
https://pub.uni-bielefeld.de/record/2003388

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Beyn W-J, Gess B, Lescot P, Röckner M. The Global Random Attractor for a Class of Stochastic Porous Media Equations. Communications in Partial Differential Equations. 2011;36(3):446-469.
Beyn, W. - J., Gess, B., Lescot, P., & Röckner, M. (2011). The Global Random Attractor for a Class of Stochastic Porous Media Equations. Communications in Partial Differential Equations, 36(3), 446-469. https://doi.org/10.1080/03605302.2010.523919
Beyn, W. - J., Gess, B., Lescot, P., and Röckner, M. (2011). The Global Random Attractor for a Class of Stochastic Porous Media Equations. Communications in Partial Differential Equations 36, 446-469.
Beyn, W.-J., et al., 2011. The Global Random Attractor for a Class of Stochastic Porous Media Equations. Communications in Partial Differential Equations, 36(3), p 446-469.
W.-J. Beyn, et al., “The Global Random Attractor for a Class of Stochastic Porous Media Equations”, Communications in Partial Differential Equations, vol. 36, 2011, pp. 446-469.
Beyn, W.-J., Gess, B., Lescot, P., Röckner, M.: The Global Random Attractor for a Class of Stochastic Porous Media Equations. Communications in Partial Differential Equations. 36, 446-469 (2011).
Beyn, Wolf-Jürgen, Gess, Benjamin, Lescot, Paul, and Röckner, Michael. “The Global Random Attractor for a Class of Stochastic Porous Media Equations”. Communications in Partial Differential Equations 36.3 (2011): 446-469.

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