Scalar Viscous Conservation Laws in $R^2$
Vol. 10 No. 4 (2015) P.553~P.574
In this paper, we follow the framework of construction of Green's function for Boltzmann equation
in  to establish the pointwise structure for the stability of shock profile for scalar viscous conservation law in
$R^2$. We treat the 2-D viscous conservation law like a kinetic equation, and introduce the shock front-remainder
decomposition to separate the effect coming from shock front. Based on this decomposition, we construct the
Green's function and get the pointwise structure of shock front.
Scalar conservation law, shock profile, Green’s function, shock front-remainder decomposition.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
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Revised : 2015-06-10