具有非线性耗散的阻尼薛定谔方程的渐近行为
Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation
首次发表
浏览论文内容
中文总结 AI 辅助
研究质量次临界阻尼薛定谔方程，证明非线性解的最优$L^2$衰减率与线性解一致，并给出任意幂次散射的最优收敛率。
中文摘要 AI 辅助
我们考虑质量次临界情形下具有非线性耗散的阻尼薛定谔方程解的大时间渐近性。我们证明，即使存在非线性耗散，非线性解的最优$L^2$衰减率也与相应线性解的衰减率一致。此外，我们给出了质量次临界范围内任意幂次下散射的最优收敛率。
英文摘要
We consider large time asymptotics of solutions to the damped Schrödinger equation with the nonlinear dissipation in the mass-subcritical case. We prove that the optimal $L^2$-decay rate of the nonlinear solution coincides with that of the corresponding linear solution even in the presence of nonlinear dissipation. Moreover, we give the optimal convergence rate for scattering for any power in the mass-subcritical regime.
