一类非凸粘性平衡律方程的粘性激波解的存在性与稳定性

本文首先利用几何奇异摄动方法，证明了粘性系数充分小时一类非凸粘性平衡律方程的粘性冲击波的存在性，推广了原来在非线性项严格凸的条件下得到的结果．进而，利用谱分析和上下解方法，证明了对固定的小的粘性系数此类波是全局渐近指数稳定的，推广了反应扩散方程中经典的全局稳定性结果．

Existence and Stability of Viscous Shock Waves for Non-Convex Viscous Balance Law

In this paper, by geometric singular perturbation method, we first prove the existence of a class of viscous shock wave solutions to a scalar balance law for sufficiently small viscosity, which extends the previous results in the strictly convex nonlinearity case to nonconvex case. Further, by detailed spectral analysis and sub-and super-solution method, we show that viscous shock waves are globally asymptotically stable which extends the classical global stability result for bistable reaction-diffusion equation.