数学科学学院学术报告[2025] 035号

(高水平大学建设系列报告1057号)

报告题目：Minimal Entropy Conditions for Scalar Conservation Laws

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：2025年5月14日上午10：30-11：30

报告地点：汇星楼501

报告内容：

In 1989, Arnol’d and Kruzkov et al., posed an important open question on whether only one single convex entropy η(u) can enforce the uniqueness of the solution for one-dimensional scalar conservation laws with convex flux functions, which is called the “Minimal Entropy Conditions” by De Lellis-Otto-Westdickenberg(2004).

For these scalar conservation laws, we prove that a single entropy-entropy flux pair (η(u),q(u)) with η(u) of strict convexity is sufficient to single out an entropy solution from a broad class of weak solutions in  that satisfy the inequality: η(u)ₜ+q(u)ₓ⩽μ, controlled by some non-negative Radon measure μ (weaker than controlled by 0), in the distributional sense. Furthermore, we extend this result to the class of weak solutions in , based on the asymptotic behavior of the flux function f(u) and the entropy function η(u) at infinity. The proofs are based on the equivalence between the entropy solutions of one-dimensional scalar conservation laws and the viscosity solutions of the corresponding Hamilton-Jacobi equations, as well as the bilinear form and commutator estimates as employed similarly in the theory of compensated compactness. This is a joint work with Professor Gui-Qiang Chen.

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副研究员。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研究，曾多次到香港城市大学和牛津大学等进行学术访问。主持过国家自然科学基金青年项目，中科院多学科交叉项目等，在J. Differential Equations，AMS Quarterly of Applied Mathematics 等国内外数学期刊上，发表论文十余篇。

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邀请人：李杏

　　　 数学科学学院 

　　　　　　　　　　　2025年5月12日