Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise

Barbu V, Da Prato G, Röckner M (2012)
Journal of Mathematical Analysis and Applications 389(1): 147-164.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Barbu, Viorel; Da Prato, Giuseppe; Röckner, MichaelUniBi
Abstract / Bemerkung
In this paper one surveys and sharpens some recent results obtained by the authors on the finite time extinction property of solutions to stochastic diffusion equations of the form dX - rho Delta X-m dt = XdW and dX - rho Delta sgn Xdt = XdW, where 0 0. These equations arise as models for nonlinear diffusion processes in porous media, plasma and self-organized criticality under stochastic Gaussian perturbation. These equations can be also viewed as control systems governed by fast diffusion porous media equations with a stochastic feedback controller XdW. (C) 2011 Elsevier Inc. All rights reserved.
Stichworte
Porous media equation; Self-organized criticality; Wiener process
Erscheinungsjahr
2012
Zeitschriftentitel
Journal of Mathematical Analysis and Applications
Band
389
Ausgabe
1
Seite(n)
147-164
ISSN
0022-247X
Page URI
https://pub.uni-bielefeld.de/record/2493091

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Barbu V, Da Prato G, Röckner M. Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. Journal of Mathematical Analysis and Applications. 2012;389(1):147-164.
Barbu, V., Da Prato, G., & Röckner, M. (2012). Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. Journal of Mathematical Analysis and Applications, 389(1), 147-164. doi:10.1016/j.jmaa.2011.11.045
Barbu, V., Da Prato, G., and Röckner, M. (2012). Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. Journal of Mathematical Analysis and Applications 389, 147-164.
Barbu, V., Da Prato, G., & Röckner, M., 2012. Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. Journal of Mathematical Analysis and Applications, 389(1), p 147-164.
V. Barbu, G. Da Prato, and M. Röckner, “Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise”, Journal of Mathematical Analysis and Applications, vol. 389, 2012, pp. 147-164.
Barbu, V., Da Prato, G., Röckner, M.: Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. Journal of Mathematical Analysis and Applications. 389, 147-164 (2012).
Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. “Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise”. Journal of Mathematical Analysis and Applications 389.1 (2012): 147-164.