带有间断系数的线性标量守恒律的黎曼解形成及其稳定性

摘要

讨论了一个带有间断系数的线性标量守恒律系统在对间断系数局部线性化的过程中其黎曼解的形成及其稳定性，其中在一些特定初值的情形下其黎曼解中含有真空状态。运用特征线法来研究当间断系数局部线性化时的广义黎曼问题，并取极限来获得其黎曼解在间断系数局部线性化扰动时的稳定性以及真空的形成过程。%The formation and stability analysis of Riemann solutions to a scalar conservation law with a linear flux function involving discontinuous coefficients were considered,where the Riemann solution has a vacuum state in some particular initial data. The generalized Riemann problem was investigated with the method of characteristics by adopting the local linearization technique to treat the discontinuous coefficient. In addition, the stability of the Riemann solutions and the formation of vacuum state can be obtained in the limit process.