中科院数学与系统科学研究院
数学研究所
学术报告会
报告人：杨汉春教授（云南大学）
题 目：New Developments and Applications of Delta Shock Waves
时 间：11.24 (星期二) , 16:30-17:30
地 点：数学院南楼N913室
摘要 :
In this work, we established a theory of delta shock waves with Dirac delta functions developing in both state variables for a class of nonstrictly hyperbolic systems of conservation laws. Firstly, we solved the Riemann problems for the system under consideration. In solutions, we found a kind of delta shock waves on which both state variables simultaneously contain the Dirac delta functions. The generalized Rankine-Hugoniot relation and entropy condition were proposed to solve the delta shock waves. Secondly, we showed all of the existence and stability of solutions including the delta shock waves to reasonable viscous perturbations. Thirdly, we exhibited the generality and practicability of our theory on the delta shock waves which can be successfully applied to some systems investigated by the previous authors. Finally, we presented the numerical simulations coinciding with theoretical analysis.
