Semi-Classical Analysis for Hartree Equations in Some Supercritical Cases
Semi-Classical Analysis for Hartree Equations in Some Supercritical Cases
复制标题
一些超临界情况下Hartree方程的半经典分析
DOI：
10.1007/s00023-007-0328-6
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Satoshi Masaki
中科院分区：
文献类型：
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作者：
Satoshi Masaki
研究了Hartree方程的半经典极限，该方程具有聚焦点。在焦散线附近存在一个临界指标，表明非线性效应的影响在亚临界情况下（称为线性焦散线情况）可以忽略，而在临界情况下（非线性焦散线情况）则不存在。在某些超临界情形下，我们给出了超越焦散线的渐近行为，这些情形引起了很强的非线性效应。
We study the semi-classical limit of the Hartree equation, which has focusing at a point. There exists a critical index indicating nonlinear effect around the caustic, and it is known that the influence by the nonlinearity is negligible in subcritical case (called linear caustic case), and that it is not in critical case (nonlinear caustic case). We give the asymptotic behavior beyond caustic in some supercritical cases which give rise to very strong nonlinear effect.