Local tracking and stability for degenerate viscous shock waves

Abstract. We study the pointwise behavior of perturbed degenerate (sonic) shock waves for scalar conservation laws with non-constant diusion. Building on the point-wise Green's function approach of [ZH], we extend the linear analysis to an equation with non-integrable coecients. In lieu of working with the integrated equation, we employ a tracking mechanism that we expect will allow degenerate waves to be incorporated into the general framework for nondegenerate systems [ZH]. 1