Euler-Poisson equations for semiconductor models with sonic boundary


主题:   Euler-Poisson equations for semiconductor models with sonic boundary主讲人:   梅茗地点:   松江校区2号学院楼331理学院报告厅时间:   2017-07-09 15:00:00组织单位:   东华大学非线性科学研究所

主讲人简介:梅茗,加拿大McGill大学Adjunct Professor及Champlain学院的终身教授。东北师范大学“东师学者”讲座教授及吉林省“长白山学者”讲座教授。1996年博士毕业于日本国立金泽大学, 师从Akitaka Matsumura教授。梅茗教授的研究领域为非线性偏微分方程。主要从事流体力学中半导体偏微分方程和生物数学中带时滞反应扩散方程研究,在Archive Rational Math. Mech., SIAM J. Math. Anal., J. DifferentialEquations, Commun. PDEs 等学术刊物上公开发表论文70余篇,是4家SCI国际数学杂志的编委。

内容摘要:In this talk, we consider the well-posedness, ill-posedness and the regularity of stationary solutions to Euler-Poisson equations with sonic boundary for semiconductor models, andprove that,  when the doping profile is subsonic,  the corresponding system with sonic boundary possess a unique interior subsonic solution, and atleast one interior supersonic solution; and if the relaxation time is large andthe doping profile is a small perturbation of constant, then the equationsadmit infinitely many interior transonic shock solutions; while, if the relaxation time is small enough and the doping profile is a subsonic constant,then the equations admits infinitely many interior C^1 smooth transonic solutions,and no transonic shock solution exists. When the doping profile is supersonic,we show that the system does not hold any subsonic solution; furthermore, thesystem doesn’t admit any supersonic solution or any transonic solution if sucha supersonic doping profile is small enough or the relaxation time is small,but it has at least one supersonic solution and infinitely many transonic solutions if the supersonic doping profile is close to the sonic line and the relaxation time is large. The interior subsonic/supersonic solutions all are globally C^{1/2}-Holder continuous, and the Holder exponent 1/2 is optimal. The non-existence of any type solutions in the case of small doping profile orsmall relaxation time indicates that the semiconductor effect for the system is remarkable and cannot be ignored. The proof for the existence ofsubsonic/supersonic solutions is the technical compactness analysis combining the energy method and the phase-plane analysis, while the approach for the existence of multiple transonic solutions is constructed. The results obtained significantly improve and develop the existing studies. 

This is a recent joint work with Jingyu Li, Guojing Zhangand Kaijun Zhang.

讲座主持:秦玉明 教授


视频:   摄影: 撰写:秦玉明  信息员:唐晓亮  编辑:吴彦