Nonintegrable perturbations of scalar viscous shock profiles

摘要

Solutions of scalar viscous conservation laws whose initial data are bounded and tend at x = ± ∞ to values that may be connected by a shock profile are shown to converge in L~∞ to a time-dependent translation of that profile. Unlike the standard theory, the initial data is not restricted to be an L~1 perturbation of the shock profile, and the translation may not be linear in time. Estimates for the translation are obtained.