Title: $L^2$-contraction and asymptotic stability of large shock for scalar viscous conservation laws Show Chinese title

Title: $L^2$-收缩和大激波在标量粘性守恒定律中的渐近稳定性

Abstract: We investigate $L^2$-contraction and time-asymptotic stability of large shock for scalar viscous conservation laws with polynomial flux. For the strictly convex flux $f(u)=u^p $ with $2\leq p \leq 4$, we can prove $L^2$-contraction and time-asymptotic stability of arbitrarily large viscous shock profile in $H^1$-framework by using $a$-contraction method with time-dependent shift and suitable weight function. Additionally, if the initial perturbation belongs to $L^1$, then $L^2$ time-asymptotic decay rate $t^{-\frac{1}{4}}$ can be obtained. Show Chinese abstract

Abstract: 我们研究标量粘性守恒律中多项式通量的$L^2$-收缩和大激波的时间渐近稳定性。 对于严格凸的通量$f(u)=u^p $且具有$2\leq p \leq 4$，我们可以通过使用时间依赖位移的$a$-收缩方法和合适的权函数，在$H^1$-框架中证明任意大的粘性激波解的$L^2$-收缩和时间渐近稳定性。 此外，如果初始扰动属于$L^1$，则可以得到$L^2$时间渐近衰减率$t^{-\frac{1}{4}}$。