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Izvestiya: Mathematics, 2012, Volume 76, Issue 2, Pages 245–274
DOI: https://doi.org/10.1070/IM2012v076n02ABEH002582 (Mi im4469) 		 
The far-field asymptotics of solutions of a fractional non-linear equation

E. I. Kaikinaa, P. I. Naumkina, I. A. Shishmarevb

a National Autonomous University of Mexico, Institute of Mathematics
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
English version PDF (411 kB) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n02ABEH002582
Abstract: We obtain the asymptotic behaviour of solutions of the Cauchy problem for a fractional non-linear equation. We show that the remainder term in the asymptotic formula is also the remainder in the far field, that is, as the spatial and temporal coordinates tend to infinity simultaneously. We also consider the case in which the Cauchy data are not small.
Keywords: far-field asymptotic behaviour, non-linear heat equation, critical non-linearity.
Received: 18.02.2010
Revised: 28.02.2011
Bibliographic databases:
Document Type: Article
UDC: 517.9+535.5
MSC: Primary 35R11; Secondary 26A33, 34A08
Language: English
Original paper language: Russian
Citation: E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “The far-field asymptotics of solutions of a fractional non-linear equation”, Izv. Math., 76:2 (2012), 245–274
Citation in format AMSBIB
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\by E.~I.~Kaikina, P.~I.~Naumkin, I.~A.~Shishmarev
\paper The far-field asymptotics of solutions of a~fractional non-linear equation
\jour Izv. Math.
\yr 2012
\vol 76
\issue 2
\pages 245--274
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  • https://www.mathnet.ru/eng/im/v76/i2/p37
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