Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

Barbu V, Röckner M, Russo F (2011)
Probability Theory and Related Fields 151(1-2): 1-43.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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DOI
Autor*in
Barbu, Viorel; Röckner, MichaelUniBi; Russo, Francesco
Einrichtung
Fakultät für Mathematik
Abstract / Bemerkung
We consider a possibly degenerate porous media type equation over all of R(d) with d = 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution.
Stichworte
representation; Singular degenerate porous media type equation; Probabilistic
Erscheinungsjahr
2011
Zeitschriftentitel
Probability Theory and Related Fields
Band
151
Ausgabe
1-2
Seite(n)
1-43
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/2454846

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Barbu V, Röckner M, Russo F. Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields. 2011;151(1-2):1-43.
Barbu, V., Röckner, M., & Russo, F. (2011). Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields, 151(1-2), 1-43. doi:10.1007/s00440-010-0291-x
Barbu, Viorel, Röckner, Michael, and Russo, Francesco. 2011. “Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case”. Probability Theory and Related Fields 151 (1-2): 1-43.
Barbu, V., Röckner, M., and Russo, F. (2011). Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields 151, 1-43.
Barbu, V., Röckner, M., & Russo, F., 2011. Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields, 151(1-2), p 1-43.
V. Barbu, M. Röckner, and F. Russo, “Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case”, Probability Theory and Related Fields, vol. 151, 2011, pp. 1-43.
Barbu, V., Röckner, M., Russo, F.: Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields. 151, 1-43 (2011).
Barbu, Viorel, Röckner, Michael, and Russo, Francesco. “Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case”. Probability Theory and Related Fields 151.1-2 (2011): 1-43.
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