Sharp Pointwise Bounds for Perturbed Viscous Shock Waves
Pointwise Asymptotic Behavior of Perturbed Viscous Shock Profiles
Refining previous work in \cite{Z.3, MaZ.3, Ra, HZ, HR}, we derive sharp
pointwise bounds on behavior of perturbed viscous shock profiles
for large-amplitude Lax or overcompressive type shocks and physical viscosity.
These extend well-known results of Liu \cite{Liu97}
obtained by somewhat different techniques for small-amplitude Lax type
shocks and artificial viscosity, completing a program set out in \cite{ZH}.
As pointed out in \cite{Liu91, Liu97}, the key to obtaining sharp bounds
is to take account of cancellation associated with the property
that the solution decays faster along characteristic than in other
directions.
Thus, we must here estimate characteristic derivatives for the entire
nonlinear perturbation, rather than judicially chosen parts
as in \cite{Ra, HR}.
a requirement that greatly complicates the analysis.
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