Geodesic
The far-field asymptotics of solutions of a~fractional non-linear equation
Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 245-274

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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. 
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     title = {The far-field asymptotics of solutions of a~fractional non-linear equation},
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E. I. Kaikina; P. I. Naumkin; I. A. Shishmarev. The far-field asymptotics of solutions of a~fractional non-linear equation. Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 245-274. http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a1/