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Long-time behavior for the 1d NLS with a delta potential
发布时间: 2018-07-21     23:30   【返回上一页】 发布人:Jason Murphy


北京师范大学数学科学学院

 

 

偏微分方程学术报告 

 

 

报告题目:Long-time behavior for the 1d NLS with a delta potential

 

报告人:Prof. Jason Murphy (Missouri University of Science and Technology)

 

时间地点:2018723日下午3:30-4:30 后主楼1124

 

邀请人:薛留堂

 

报告摘要:In this talk, I will discuss some recent joint work with S. Masaki and J. Segata.  We first considered the 1d cubic NLS with a repulsive delta potential and established long-time decay and modified scattering for small initial data in a weighted Sobolev space.  Next, we considered the case of an attractive delta potential with a mass-supercritical nonlinearity.  In this case one has small solitary waves and does not expect small-data scattering.  Instead, we prove the asymptotic stability of these small solitary waves in the energy space. That is, any small solution decouples into a sum of a small solitary wave plus a radiation part as time tends to infinity.