A SHOCK LAYER IN PARABOLIC PERTURBATIONS OF A SCALAR CONSERVATION LAW

[摘要] A definition of a shock layer of thickness $delta$ is proposed when a parabolic perturbation is applied to a scalar conservation law. The asymptotic equality $deltaasympsqrt{varepsilon}$ is established, where $varepsilon$ denotes viscosity. This equality is proved to be optimal. Nevertheless, the equality $deltaasympvarepsilon$ is also proved to be valid for a class of shocks in accordance with the Mises conjecture.AMS 2000 Mathematics subject classification: Primary 35L67. Secondary 35K65

[学科分类] 数学（综合）

[关键词] Riemann problem;shock;parabolic perturbation