Stochastic porous media equations in ℝ<sup>d</sup>

Barbu V, Röckner M, Russo F (2015)
Journal de Mathématiques Pures et Appliquées 103(4): 1024-1052.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Barbu, Viorel; Röckner, MichaelUniBi; Russo, Francesco
Abstract / Bemerkung
Existence and uniqueness of solutions to the stochastic porous media equation dX - Delta psi(X)dt = XdW in R-d are studied. Here, W is a Wiener process, psi is a maximal monotone graph in R x R such that psi(r) <= C vertical bar r vertical bar(m), for all r is an element of R. In this general case, the dimension is restricted to d >= 3, the main reason being the absence of a convenient multiplier result in the space H = {phi is an element of S' (R-d); vertical bar xi vertical bar (F phi)(xi) is an element of L-2(R-d)}, for d <= 2. When psi is Lipschitz, the well-posedness, however, holds for all dimensions on the classical Sobolev space H-1(R-d). If psi(r)r >= rho vertical bar r vertical bar(m+1) and m = d-2/d+2, we prove the finite time extinction with strictly positive probability. (C) 2014 Elsevier Masson SAS. All rights reserved.
Stichworte
Maximal monotone graph; Wiener process; Stochastic; Porous media; Distributions
Erscheinungsjahr
2015
Zeitschriftentitel
Journal de Mathématiques Pures et Appliquées
Band
103
Ausgabe
4
Seite(n)
1024-1052
ISSN
0021-7824
Page URI
https://pub.uni-bielefeld.de/record/2733472

Zitieren

Barbu V, Röckner M, Russo F. Stochastic porous media equations in ℝ<sup>d</sup>. Journal de Mathématiques Pures et Appliquées. 2015;103(4):1024-1052.
Barbu, V., Röckner, M., & Russo, F. (2015). Stochastic porous media equations in ℝ<sup>d</sup>. Journal de Mathématiques Pures et Appliquées, 103(4), 1024-1052. doi:10.1016/j.matpur.2014.10.004
Barbu, V., Röckner, M., and Russo, F. (2015). Stochastic porous media equations in ℝ<sup>d</sup>. Journal de Mathématiques Pures et Appliquées 103, 1024-1052.
Barbu, V., Röckner, M., & Russo, F., 2015. Stochastic porous media equations in ℝ<sup>d</sup>. Journal de Mathématiques Pures et Appliquées, 103(4), p 1024-1052.
V. Barbu, M. Röckner, and F. Russo, “Stochastic porous media equations in ℝ<sup>d</sup>”, Journal de Mathématiques Pures et Appliquées, vol. 103, 2015, pp. 1024-1052.
Barbu, V., Röckner, M., Russo, F.: Stochastic porous media equations in ℝ<sup>d</sup>. Journal de Mathématiques Pures et Appliquées. 103, 1024-1052 (2015).
Barbu, Viorel, Röckner, Michael, and Russo, Francesco. “Stochastic porous media equations in ℝ<sup>d</sup>”. Journal de Mathématiques Pures et Appliquées 103.4 (2015): 1024-1052.

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