Malliavin Calculus for the stochastic Cahn- Hilliard/Allen-Cahn equation with unbounded noise diffusion
Name:
Publisher version
View Source
Access full-text PDFOpen Access
View Source
Check access options
Check access options
Affiliation
University of Chester; Foundation for Research and Technology; University of CretePublication Date
2018-05-08
Metadata
Show full item recordAbstract
The stochastic partial di erential equation analyzed in this work, is motivated by a simplified mesoscopic physical model for phase separation. It describes pattern formation due to adsorption and desorption mechanisms involved in surface processes, in the presence of a stochastic driving force. This equation is a combination of Cahn-Hilliard and Allen-Cahn type operators with a multiplicative, white, space-time noise of unbounded di usion. We apply Malliavin calculus, in order to investigate the existence of a density for the stochastic solution u. In dimension one, according to the regularity result in [5], u admits continuous paths a.s. Using this property, and inspired by a method proposed in [8], we construct a modi ed approximating sequence for u, which properly treats the new second order Allen-Cahn operator. Under a localization argument, we prove that the Malliavin derivative of u exists locally, and that the law of u is absolutely continuous, establishing thus that a density exists.Citation
Antonopoulou, D., Farazakis, D., & Karali, G. D. (2018). Malliavin Calculus for the stochastic Cahn- Hilliard/Allen-Cahn equation with unbounded noise diffusion. Journal of Differential Equations, 265(7), 3168-3211.Publisher
ElsevierAdditional Links
https://www.sciencedirect.com/science/article/pii/S0022039618302699Type
ArticleLanguage
enISSN
0022-0396ae974a485f413a2113503eed53cd6c53
10.1016/j.jde.2018.05.004
Scopus Count
Collections
The following license files are associated with this item:
- Creative Commons
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by-nc-nd/4.0/