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Scattering for Radial Defocusing Inhomogeneous Bi-Harmonic SchrÖDinger Equations
Potential Analysis ( IF 1.0 ) Pub Date : 2021-01-31 , DOI: 10.1007/s11118-020-09898-6 Tarek Saanouni
中文翻译:
径向离焦非均匀双调和薛定D方程的散射
更新日期:2021-01-31
Potential Analysis ( IF 1.0 ) Pub Date : 2021-01-31 , DOI: 10.1007/s11118-020-09898-6 Tarek Saanouni
This note studies the asymptotic behavior of global solutions to the fourth-order Schrödinger equation
$$ i\dot u+{\Delta}^{2} u-F(x,u)=0 . $$Indeed, for both cases, local and non-local source term, the scattering is obtained in the defocusing mass super-critical and energy sub-critical regimes, with radial setting.
中文翻译:
径向离焦非均匀双调和薛定D方程的散射
本笔记研究四阶Schrödinger方程的整体解的渐近行为
$$ i \ dot u + {\ Delta} ^ {2} uF(x,u)= 0。$$确实,对于两种情况,局部和非局部源项,在径向设置的散焦质量超临界和能量亚临界状态下均能获得散射。