Asymptotic stability of traveling waves with shock profile for non-convex viscous scalar conservation laws, Mathematical analysis of phenomena in fluid and plasma dynamics (Japanese) (Kyoto

We consider the Cauchy problem for scalar viscous conservation laws: $u_{t}+f(u)_{x}=\mu u_{xx} $ , $x\in R, $ $t>0 $ (1.1) $u(0, x)=u_{0}(x) $ , $x\in R $ , (1.2) where $\mu\iota $ is a positive $c $)$nstant $ and the initial data $u_{0}(x) $ is asympto,ically constant as $xarrow\pm\infty $