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