数学科学学院学术报告[2024] 124号

(高水平大学建设系列报告1004号)

报告题目:Riemann Solutions with Non-selfsimilar Structures for Multi-dimensional Scalar Conservation Laws with Source Terms

报告人：曹高伟 副研究员（中国科学院精密测量科学与技术创新研究院）

报告时间：2024年11月25日上午10:30-11:30

报告地点：深圳大学粤海校区汇星楼一楼1号教室

报告内容：This talk mainly introduces the Riemann solutions with non-selfsimilar structures for the multi-dimensional scalar conservation laws with source terms, especially including the expressions of multi-dimensional shock waves and rarefaction waves; these can be viewed in the following two aspects:

(i) Solutions of non-selfsimilar structures. For the Riemann problem of multi-dimensional cases, the initial discontinuities highly influence the structures of Riemann solutions. Instead of the selfsimilar structures enforced by the straight initial discontinuities, we deal with the Riemann problem with curved initial discontinuities, which necessarily yield the Riemann solutions to possess non-selfsimilar structures.

(ii) Influences of Source Terms. Compared with characteristics being straight lines in the homogeneous case, the source term curves the characteristics and hence influences the solution structures, which makes the characteristic analysis to be complicated and the expressions of shock waves and rarefaction waves to be different.

Importantly, the source term of non-Lipschitz impacts the solution structures hugely and induces two new interesting phenomena: The shock waves and rarefaction waves may disappear in a finite time and the rarefaction waves may contain some weak discontinuities in their interiors.

In addition, this talk gives a brief introduction for the suitability of the Kruzkov’s entropy conditions for the first-order quasilinear equations with non-Lipschitz source terms. These are joint works with Professors Gui-Qiang Chen, Wei Xiang, and Xiaozhou Yang.

报告人简历：曹高伟，中国科学院精密测量科学与技术创新研究院 (原中科院武汉物理与数学研究所)，副研究员。本科毕业于郑州大学数学系，博士毕业于中科院武汉物理与数学研究所，师从杨小舟研究员。主要从事双曲型守恒律方程，流体力学中欧拉方程，和随机偏微分方程的数学理论的研究，包括弱解公式，弱解的适定性，弱解的精细性质和大时间行为，黎曼问题解的构造和光滑解的公式，以及相应的随机问题；曾多次到香港城市大学和牛津大学等进行学术访问，近期访问了牛津大学讲座教授陈贵强，为期一年；在国内外数学期刊上，发表学术论文十余篇。

欢迎师生参加！

报告邀请人：张擎天

　数学科学学院

　　　　　　　　　　2024年11月22日