Linearized Stability of Extreme Shock Profiles in Systems of Conservation Laws with Viscosity

Robert L. Pego
1983 Transactions of the American Mathematical Society  
For a genuinely nonlinear hyperbolic system of conservation laws with added artificial viscosity, u, + f(u)x = euxx, we prove that traveling wave profiles for small amplitude extreme shocks (the slowest and fastest) are linearly stable to perturbations in initial data chosen from certain spaces with weighted norm; i.e., we show that the spectrum of the linearized equation lies strictly in the left-half plane, except for a simple eigenvalue at the origin (due to phase translations of the
more » ... . The weight ecx is used in components transverse to the profile, where, for an extreme shock, the linearized equation is dominated by unidirectional convection.
doi:10.2307/1999627 fatcat:6ifha4ikgrfrdlun7tpqcuxkmm