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

 

Transient anomalous sub-diffusion on bounded domains


Authors: Mark M. Meerschaert, Erkan Nane and P. Vellaisamy
Journal: Proc. Amer. Math. Soc. 141 (2013), 699-710
MSC (2010): Primary 60G52, 35Q86; Secondary 35P10
Published electronically: June 26, 2012
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Abstract: This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.


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Additional Information

Mark M. Meerschaert
Affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48823
Email: mcubed@stt.msu.edu

Erkan Nane
Affiliation: Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, Alabama 36849
Email: nane@auburn.edu

P. Vellaisamy
Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
Email: pv@math.iit.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11362-0
PII: S 0002-9939(2012)11362-0
Keywords: Fractional diffusion, Cauchy problem, tempered stable, boundary value problem.
Received by editor(s): May 2, 2011
Received by editor(s) in revised form: July 8, 2011
Published electronically: June 26, 2012
Additional Notes: The first author was partially supported by NSF grants DMS-1025486, DMS-0803360, EAR-0823965 and NIH grant R01-EB012079-01.
This paper was completed while the third author was visiting Michigan State University.
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.