Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation

We study the time-asymptotic behavior of solutions of the Schrödinger equation with nonlinear dissipation \begin{equation*} \partial _t u = i Δu + λ|u|^αu \end{equation*} in ${\mathbb R}^N$, $N\geq1$, where $λ\in {\mathbb C}$, $\Re λ<0$ and $0<α<\frac2N$. We give a precise description of the behavior of the solutions (including decay rates in $L^2$ and $L^\infty$, and asymptotic profile), for a class of arbitrarily large initial data, under the additional assumption that $α$ is sufficiently close to $\frac2N$.

No reviews yet.

No comments yet.