Chen Shuxing, academician of the Chinese Academy of Sciences and professor of Fudan University, visited Peiyang Mathematics Seminar, bringing a report about Two Dimensional Riemann Problem to teachers and students at Xingsun Building A301, Peiyang Campus of Tianjin University on the afternoon of June 6, 2019. Sun Xiaotao, Dean of School of Mathematics, presided over the Seminar.
Starting from the study of the Riemann problem of one dimensional nonlinear hyperbolic equation, Academician Chen Shuxing introduced origin and significance of Riemann problem, expounded the complete solution of one dimensional Riemann problem by Lax theorem, and summarized research methods in the study of one dimensional Riemann problem, leading the audience to think about how to study two dimensional Riemann problem.
Because of the complexity of zone and equation, the study of two dimensional Riemann problem is far more difficult than its one dimensional situation. For two dimensional Riemann problem, Chen Shuxing took the Riemann problem of two dimensional Euler equation system as an example to explain current research methods and conclusions of two dimensional Riemann problem in detail. While explaining mathematical equation, he emphasized the importance of physical background and numerical experiments in mathematical research. For this reason, Academician Chen enumerated that the study of many practical problems in real life could be transformed into the study of corresponding Riemann problems, such as dam collapse, shock reflection, back steps and so on.
Finally, Chen Shuxing enumerated some difficulties in the study of two dimensional Riemann problem. But he encouraged students to study hard without fear of difficulties when facing with difficult problems in mathematics researches.
At the end of the report, teachers and students raised their own questions in the field of their researches, either on the condition of discontinuity of non-linear hyperbola or on the two dimensional Riemann problem itself. After the collision of ideas, the audience gained a lot. With warm applause, the report came to a successful conclusion.