Asymptotic behavior of solutions to Schrodinger equations with a subcritical dissipative nonlinearity

[摘要] We study the asymptotic behavior in time of solutions to the initial value problem of the nonlinear Schrodinger equation with a subcritical dissipative nonlinearity; lambda vertical bar u vertical bar(p-1)u, where 1 < p < 1 + 2/n, n is the space dimension and. is a complex constant satisfying Im lambda < 0. We show the time decay estimates and the large-time asymptotics of the solution, when the space dimension n <= 3, p is sufficiently close to 1 + 2/n and the initial data is sufficiently small. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-01

[关键词] nonlinear Schrodinger equation;asymptotic behavior;subcritical dissipative nonlinearity