中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

偏微分方程讨论班

Speaker: 陈秀卿 教授（ 中山大学（珠海） ）

Inviter: 霍朝辉

Language: Chinese

Title: Fluid Relaxation Approximation of the Busenberg-Travis Cross-diffusion System

Time & Venue: 2025年12月03日（星期三）14：30-15：30 & 腾讯会议：307-858-567

Abstract: The Busenberg–Travis cross-diffusion system for segregating populations is approximated by the compressible Navier–Stokes–Korteweg equations on the torus, including a density-dependent viscosity and drag forces. The Korteweg term can be associated to the quantum Bohm potential. The singular asymptotic limit is proved rigorously using compactness and relative entropy methods. The novelty is the derivation of energy and entropy inequalities, which reduce in the asymptotic limit to the Boltzmann–Shannon and Rao entropy inequalities, thus revealing the double entropy structure of the limiting Busenberg–Travis system.

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Speaker: 裴龙 教授（ 中山大学（珠海） ）

Inviter: 霍朝辉

Language: Chinese

Title: Properties of traveling wave solutions to nonlinear dispersive equations

Time & Venue: 2025年12月03日（星期三）15：30-16：30 & 腾讯会议：307-858-567

Abstract: We will talk about properties of traveling wave solutions to nonlinear dispersive equations. In particular, we consider the symmetry of  traveling waves at the presence of weak dispersion. In addition, the relation between symmetry and the steady properties of solutions will be introduced.