Existence of strong solutions for stochastic porous media equation under general monotonicity conditions

Barbu V, Da Prato G, Röckner M (2009)
Annals of Probability 37(2): 428-452.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Barbu, Viorel; Da Prato, Giuseppe; Röckner, MichaelUniBi
Abstract / Bemerkung
This paper addresses the existence and uniqueness of strong solutions to stochasic porous media equations dX - Delta Psi(X)dt = B(X)dW(t) in bounded domains of R-d with Dirichlet boundary conditions. Here Psi is a maximal monotone graph in R x R (possibly multivalued) with the domain and range all of R. Compared with the existing literature on stochastic porous media equations, no growth condition on Psi is assumed and the diffusion coefficient Psi might be multivalued and discontinuous. The latter case is encountered in stochastic models for self-organized criticality or phase transition.
Stichworte
Stochastic porous media equation; convex functions; Ito's formula; Wiener process
Erscheinungsjahr
2009
Zeitschriftentitel
Annals of Probability
Band
37
Ausgabe
2
Seite(n)
428-452
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/1633933

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Barbu V, Da Prato G, Röckner M. Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Annals of Probability. 2009;37(2):428-452.
Barbu, V., Da Prato, G., & Röckner, M. (2009). Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Annals of Probability, 37(2), 428-452. doi:10.1214/08-AOP408
Barbu, V., Da Prato, G., and Röckner, M. (2009). Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Annals of Probability 37, 428-452.
Barbu, V., Da Prato, G., & Röckner, M., 2009. Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Annals of Probability, 37(2), p 428-452.
V. Barbu, G. Da Prato, and M. Röckner, “Existence of strong solutions for stochastic porous media equation under general monotonicity conditions”, Annals of Probability, vol. 37, 2009, pp. 428-452.
Barbu, V., Da Prato, G., Röckner, M.: Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Annals of Probability. 37, 428-452 (2009).
Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. “Existence of strong solutions for stochastic porous media equation under general monotonicity conditions”. Annals of Probability 37.2 (2009): 428-452.