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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity of a fractional partial differential equation driven by space-time white noise


Authors: Min Niu and Bin Xie
Journal: Proc. Amer. Math. Soc. 138 (2010), 1479-1489
MSC (2010): Primary 60H15; Secondary 26A33, 35R60
Published electronically: November 18, 2009
MathSciNet review: 2578542
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Abstract: We will deal with one dimensional stochastic fractional order partial differential equation driven by space-time white noise. The existence and uniqueness of the solution and especially some regularities of the solution are investigated. The regularities of the solution in its time and space variables depend on the relation of the fractional order of its operator and coefficients.


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Additional Information

Min Niu
Affiliation: Department of Mathematics and Mechanics, Beijing University of Science and Technology, Beijing, 100083, People’s Republic of China
Email: niuminfly@sohu.com

Bin Xie
Affiliation: International Young Researchers Empowerment Center and Department of Mathematical Sciences, Faculty of Science, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano 390-8621, Japan
Email: bxie@shinshu-u.ac.jp, bxie05@sohu.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10197-1
PII: S 0002-9939(09)10197-1
Keywords: Space-time white noise, fractional differential operator, regularity, H\"{o}lder continuity, strong differentiability
Received by editor(s): June 3, 2009
Published electronically: November 18, 2009
Additional Notes: The first author was supported in part by the National Natural Science Foundation of China under grant No. 10871202.
The second author was supported in part by the Grant-in-Aid for young scientists (start-up) 20840019 (JSPS) and Grant-in-Aid for young scientists (B) 21740067(MEXT)
Communicated by: Walter Craig
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.