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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-09-10197-1

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.