时间：2025年5月17日10:00

地点：东校区第二教学楼2106（学术报告厅）

报告人：冯跃红 北京工业大学     

报告摘要：

This talk is concerned with the relaxation-time limits to multiple-dimensional radial steady hydrodynamic model of semiconductors in the form of Euler-Poisson equations with sonic or non-sonic boundary as the relaxation-time$\tau\to\infty$ and $\tau\to0^+$ respectively, where the sonic boundary is thecritical case, which is difficult, because of the degeneracy at the boundaryand the formation of boundary layers. For the case of $\tau\rightarrow\infty$, after showing the boundness of density by using the divergence form, we first prove the convergence of the solutions to their nontrivial asymptotic stateswith the convergence order  O(\tau^{-\frac{1}{2}})$ in $L^\infty$-sense. In order to overcome the degeneracy caused by the critical sonic boundary, we technically introduce an inverse transformation to remove the second-order degeneracy, and observe the advantage of first-order degeneracy due to the monotonicity of this transformation. Moreover, when  \tau\rightarrow0^+$with different boundary values, where the boundary layers appear, we show the strong convergence order $O(\tau )$ or $O(\tau^{1-\varepsilon})$ for different boundary cases. In order to overcome the difficulty cased by the boundary layers, we propose a new technique in asymptotic limit analysis and recognize the width of the boundary layers as $O(\tau)$. These new proposed methods develop and improve the existing studies. This talk is based on the collaboration work with Haifeng Hu, Ming Mei, Gantumur Tsogtgerel and Guojing Zhang.

报告人简介：

冯跃红，北京工业大学副教授，硕士生导师，研究生教学督导专家、应用数学研究所副所长。法国克莱蒙大学中、法双博士学位。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。与王术教授合作编著出版《电磁流体动力学方程与奇异摄动理论》现代数学基础丛书。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，发表SCI论文30余篇。部分研究成果发表在《SIAMJ. Math. Anal.》，《Math. Models Methods Appl. Sci.》，《中国科学·数学》，《J.Differential Equations》，《Nonlinearity》等期刊上。