Singular-degenerate Multivalued Stochastic Fast Diffusion Equations

Gess B, Röckner M (2015)
Siam Journal on Mathematical Analysis 47(5): 4058-4090.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We consider singular-degenerate, multivalued stochastic fast diffusion equations with multiplicative Lipschitz continuous noise. In particular, this includes the stochastic sign fast diffusion equation arising from the Bak-Tang-Wiesenfeld model for self-organized criticality. A well-posedness framework based on stochastic variational inequalities (SVI) is developed, characterizing solutions to the stochastic sign fast diffusion equation, previously obtained in a limiting sense only. Aside from generalizing the SVI approach to stochastic fast diffusion equations we develop a new proof of well-posedness, applicable to general diffusion coefficients. In case of linear multiplicative noise, we prove the existence of (generalized) strong solutions, which entails higher regularity properties of solutions than previously known.
Stichworte
singular-degenerate SPDE
Erscheinungsjahr
2015
Zeitschriftentitel
Siam Journal on Mathematical Analysis
Band
47
Ausgabe
5
Seite(n)
4058-4090
ISSN
0036-1410
eISSN
1095-7154
Page URI
https://pub.uni-bielefeld.de/record/2901045

Zitieren

Gess B, Röckner M. Singular-degenerate Multivalued Stochastic Fast Diffusion Equations. Siam Journal on Mathematical Analysis. 2015;47(5):4058-4090.
Gess, B., & Röckner, M. (2015). Singular-degenerate Multivalued Stochastic Fast Diffusion Equations. Siam Journal on Mathematical Analysis, 47(5), 4058-4090. doi:10.1137/151003726
Gess, B., and Röckner, M. (2015). Singular-degenerate Multivalued Stochastic Fast Diffusion Equations. Siam Journal on Mathematical Analysis 47, 4058-4090.
Gess, B., & Röckner, M., 2015. Singular-degenerate Multivalued Stochastic Fast Diffusion Equations. Siam Journal on Mathematical Analysis, 47(5), p 4058-4090.
B. Gess and M. Röckner, “Singular-degenerate Multivalued Stochastic Fast Diffusion Equations”, Siam Journal on Mathematical Analysis, vol. 47, 2015, pp. 4058-4090.
Gess, B., Röckner, M.: Singular-degenerate Multivalued Stochastic Fast Diffusion Equations. Siam Journal on Mathematical Analysis. 47, 4058-4090 (2015).
Gess, Benjamin, and Röckner, Michael. “Singular-degenerate Multivalued Stochastic Fast Diffusion Equations”. Siam Journal on Mathematical Analysis 47.5 (2015): 4058-4090.