The far-field asymptotics of solutions of a~fractional non-linear equation

E. I. Kaikina ; P. I. Naumkin ; I. A. Shishmarev

Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 245-274.

Résumé

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.

Détail

Keywords: far-field asymptotic behaviour, non-linear heat equation, critical non-linearity.

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