General extinction results for stochastic partial differential equations and applications

Röckner M, Wang F-Y (2013)
Journal Of The London Mathematical Society 87(2): 545-560.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Wang, Feng-Yu
Abstract / Bemerkung
Let L be a positive-definite self-adjoint operator on the L-2 space associated to a sigma-finite measure space. Let H be the dual space of the domain of L-1/2 with respect to L-2(mu). By using an Ito-type inequality for the H-norm and an integrability condition for the hyperbound of the semigroup P-t:e(-Lt), general extinction results are derived for a class of continuous adapted processes on H. Main applications include stochastic and deterministic fast diffusion equations with fractional Laplacians. Furthermore, we prove exponential integrability of the extinction time for all space dimensions in the singular diffusion version of the well-known Zhang model for self-organized criticality, provided the noise is small enough. Thus, we obtain that the system goes to the critical state in finite time in the deterministic case and with probability 1 in finite time in the stochastic case.
Erscheinungsjahr
2013
Zeitschriftentitel
Journal Of The London Mathematical Society
Band
87
Ausgabe
2
Seite(n)
545-560
ISSN
0024-6107
Page URI
https://pub.uni-bielefeld.de/record/2584618

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Röckner M, Wang F-Y. General extinction results for stochastic partial differential equations and applications. Journal Of The London Mathematical Society. 2013;87(2):545-560.
Röckner, M., & Wang, F. - Y. (2013). General extinction results for stochastic partial differential equations and applications. Journal Of The London Mathematical Society, 87(2), 545-560. doi:10.1112/jlms/jds066
Röckner, M., and Wang, F. - Y. (2013). General extinction results for stochastic partial differential equations and applications. Journal Of The London Mathematical Society 87, 545-560.
Röckner, M., & Wang, F.-Y., 2013. General extinction results for stochastic partial differential equations and applications. Journal Of The London Mathematical Society, 87(2), p 545-560.
M. Röckner and F.-Y. Wang, “General extinction results for stochastic partial differential equations and applications”, Journal Of The London Mathematical Society, vol. 87, 2013, pp. 545-560.
Röckner, M., Wang, F.-Y.: General extinction results for stochastic partial differential equations and applications. Journal Of The London Mathematical Society. 87, 545-560 (2013).
Röckner, Michael, and Wang, Feng-Yu. “General extinction results for stochastic partial differential equations and applications”. Journal Of The London Mathematical Society 87.2 (2013): 545-560.

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