Local tracking and stability for degenerate viscous shock waves
Local tracking and stability for degenerate viscous shock waves
We study the pointwise behavior of perturbed degenerate (sonic) shock waves
for scalar conservation laws with nonconstant diffusion. Building on the
pointwise Green's function approach of Zumbrun and Howard (Indiana U. Math. J.
47(3) (1998) 741), we extend the linear analysis to an equation with nonintegrable
coefficients. 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.
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