Scalar Viscous Conservation Laws in $R^2$
by Shijin Deng   Weike Wang  

Vol. 10 No. 4 (2015) P.553~P.574

ABSTRACT

In this paper, we follow the framework of construction of Green's function for Boltzmann equation in [12] 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.

KEYWORDS
Scalar conservation law, shock profile, Green’s function, shock front-remainder decomposition.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 82C40.

MILESTONES

Received: 2015-03-31
Revised : 2015-06-10
Accepted: 2015-06-10

Download Full Content