Title: Viscous approximation of triangular system in 1-d with nonlinear viscosity Show Chinese title

Title: 一维三角系统的粘性逼近，具有非线性粘性

Abstract: We study the vanishing viscosity limit for $2\times2$ triangular system of hyperbolic conservation laws when the viscosity coefficients are non linear. In this article, we assume that the viscosity matrix $B(u)$ is commutating with the convective part $A(u)$. We show the existence of global smooth solution to the parabolic equation satisfying uniform total variation bound in $\varepsilon$ provided that the initial data is small in $BV$. This extends the previous result of Bianchini and Bressan [Commun. Pure Appl. Anal. (2002)] which was considering the case $B(u)=I$. Show Chinese abstract

Abstract: 我们研究了当粘性系数是非线性时，$2\times2$三角双曲守恒律系统的粘性消失极限问题。本文假设粘性矩阵$B(u)$与对流部分$A(u)$是可交换的。我们证明了如果初始数据在$BV$中足够小，则抛物方程具有全局光滑解，并且满足$\varepsilon$中的均匀总变差界。这推广了Bianchini和Bressan[Commun. Pure Appl. Anal. (2002)]先前的结果，他们考虑的是情况$B(u)=I$。