Pointwise Green's function approach to stability for scalar conservation laws

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We study the pointwise behavior of perturbations from a viscous shock solution to a scalar conservation law, obtaining an estimate independent of shock strength. We find that for a perturbation with initial data decaying algebraically or slower, the perturbation decays in time at the rate of decay of the integrated initial data in any L^P norm, p > 1. Stability in any L^P norm is a direct consequence. The approach taken is that of obtaining pointwise estimates on the perturbation through a Duhamel's principle argument that employs recently developed pointwise estimates on the Green's function for the linearized equation.

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