Department of Mathematics and Statistics
University of Massachusetts Amherst
Joint with Professor Zhouping Xin.
We study the asymptotic equivalence of a general linear system
of one-dimensional conservation laws and the corresponding relaxation
model proposed by Jin and Xin [Comm. Pure Applied Math., 48
(1995), no. 3, 235-276] in the limit of small relaxation rate.
The main interest is this asymptotic equivalence in the presence
of physical boundaries. We identify and rigorously justify a
necessary and sufficient condition (which we refer to Stiff
Kreiss Condition) on the boundary condition to guarantee the
uniform well-posedness of the initial boundary value problem
for the relaxation system independent of the rate of relaxation.
The Stiff Kreiss Condition is derived and simplified by using
a normal mode analysis and a conformal mapping theorem. The
asymptotic convergence and boundary layer behavior are studied
by Laplace transform and a matched asymptotic analysis.