Type: Article

The far-field asymptotics of solutions of a nonlinear equation with a fractional derivative

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

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.