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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

The dynamics of the mean mass of a solution of the stochastic porous media equation


Author: S. A. Mel’nik
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 153-161
MSC (2010): Primary 60F10; Secondary 62F05
Published electronically: March 21, 2014
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Abstract: Conditions are found under which the mean mass of a non-trivial solution of the Cauchy problem for the stochastic porous media equation becomes infinitely large during a finite time.


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Additional Information

S. A. Mel’nik
Affiliation: Department of Probability Theory and Mathematical Statistics, Institute of Applied Mathematics and Mechanics, National Academy of Science of Ukraine, R. Luxemburg Street, 74, Donetsk, 83114, Ukraine
Email: melnik@iamm.ac.donetsk.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2014-00910-2
PII: S 0094-9000(2014)00910-2
Keywords: Stochastic partial differential equation
Received by editor(s): December 13, 2011
Published electronically: March 21, 2014
Additional Notes: This research was supported by the State Fund for Fundamental Researches of Ukraine and Russian Fund for Fundamental Researches, grant $Φ$40.1/023
Article copyright: © Copyright 2014 American Mathematical Society