Nonlinear asymptotic stability of general small-amplitude viscous Laxian shock waves
For a system of viscous conservation laws \(u_t+f(u)_x= \mu u_{xx}\) with a general hyperbolic inviscid part the author proves asymptotic stability of small-amplitude Laxian travelling-wave profiles for initial perturbations of the form \((U_0)_x\) where the function \(U_0\) has a small norm in \(H^{2,2}\).
small-amplitude Laxian travelling-wave profiles
scientific article; zbMATH DE number 1206640