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学术报告Structural stability of interior subsonic steady-states to hydrodynamic model for semiconductors with sonic boundary


报告人:冯跃红 副教授

主持人:张晓颖 院长

时 间:2023年7月21日星期五,下午15:00–16:00

地 点:理学院315会议室


报告人简介:冯跃红,副教授,硕士生导师。2014年9月毕业于法国克莱蒙大学,获中、法双博士学位;同年10月到北京工业大学工作,2015年被评为北京工业大学优博。目前主要从事应用科学中的非线性偏微分方程定解问题解的适定性和渐近机制等领域的研究工作,在SIAM. J. Math. Anal.、M3AS、JNS、JDE等期刊发表SCI论文20余篇;主持和参加多项国家自然科学基金和北京市自然科学基金。

观点综述:For the stationary hydrodynamic model for semiconductors with sonic boundary, represented by Euler-Poisson equations, it possesses the various physical solutions including interior subsonic solutions/interior supersonic solutions/shock transonic solutions/$C^1$-smooth transonic solutions. However, the structural stability for these physical solutions is challenging and has remained open as we know. In this talk, we give the structural stability of interior subsonic solutions when the doping profiles are restricted in the subsonic region. The main result is proved by using the local (weighted) singularity analysis and the monotonicity argument. Both the result itself and techniques developed here will give us some truly enlightening insights into our follow-up study on the structural stability of the remaining types of solutions. This is a joint work with Haifeng Hu and Ming Mei.