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 Howard and Zumbrun, 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 L^p norms, p >= 1.

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