Pointwise estimates and stability for degenerate viscous shock waves
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We study the pointwise behavior of perturbed degenerate (sonic) shock waves for scalar conservation laws with constant diffusion. Building on the pointwise Green's function approach of [H1-3], [ZH], we extend the linear analysis to an equation with non-integrable coefficients, arriving at an estimate on linearized perturbations believed sharp to a possible error of size log t. Nonlinear stability for degenerate waves follows in all Lpnorms, p 1.