Type: Article

A boundary-value problem for a nonlinear equation with a fractional derivative

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

Abstract:

We consider a problem on a half-line with a Neumann-type boundary condition. We prove the global existence of solutions and find the leading term of their large-time asymptotic expansion. The case of large initial data and critical non-linearity is considered in the case when the non-linear term of the equation decays in time as rapidly as the linear terms.