广州数学大讲坛第二期

第十二讲——华南理工大学朱长江教授学术报告


题目:Stability of planar rarefaction wave for a 2D hyperbolic-elliptic coupled system on half space

时间:2022年5月9日(周一)下午14:20-15:20

地点:腾讯会议(会议ID:936556756)

报告人:朱长江

报告摘要:In this talk, we will introduce the asymptotic stability of solution to an initial-boundary value problem for a hyperbolic-elliptic coupling system on two-dimensional half space. We show that the solution to the problem converges to the corresponding planar rarefaction wave as time tends to infinity. To our knowledge, the stability result of planar rarefaction wave on half space focus primarily on the single viscosity conservation law because the rarefaction wave (one-dimensional diffusion wave) of the corresponding one-dimensional problem to scalar viscosity conservation law is known. In other words, for a general high dimensional system of equations, we cannot obtain the stability of planar rarefaction wave on half space because we cannot construct the rarefaction wave of the corresponding one-dimensional problem. In this paper, we use the structure of the hyperbolic-elliptic coupling system to obtain the monotonic rarefaction wave of the corresponding one-dimensional problem, and hence give the stability of the plane rarefaction wave on half space.

This is a joint work with Minyi Zhang.

报告人简介:

朱长江,博士,华南理工大学教授、博士生导师,享受国务院政府特殊津贴,国家杰出青年基金获得者,国际数学学术期刊《Kinetic and Related Models》、《Acta Mathematica Scientia》中英文版等杂志编委,《数学教育学报》副主编,教育部高等学校数学类教学指导委员会委员,教育部“创新团队发展计划”、国家自然科学基金重点项目、国家级教学团队、国家级一流本科专业、国家级精品课程、精品资源共享课程和一流本科课程负责人,全国百篇优秀博士学位论文指导教师。主持完成的研究成果获教育部自然科学奖二等奖,教学成果两次获国家级教学成果奖二等奖。2012年被评为全国优秀科技工作者,2017年入选国家“万人计划”教学名师,2020年获中国教师发展基金会杰出教学奖。