School of Mathematics and Computer Sciences
Jianghan University
Wuhan 430056, China
email: zhangqingling2002@163.com
Qingling Zhang
Abstract:
We study the stability of Riemann solutions to pressureless Euler
equations with Coulomb-type friction under the nonlinear
approximation of flux functions with one parameter. The approximated
system can be seen as the generalized Chaplygin pressure Aw-Rascle
model with Coulomb-type friction, which is also equivalent to the
nonsymmetric system of Keyfitz-Kranzer type with generalized
Chaplygin pressure and Coulomb-type friction. Compared with the
original system. The approximated system is strictly hyperbolic,
which has one eigenvalue genuinely nonlinear and the other linearly
degenerate. Hence, the structure of its Riemann solutions is much
different from the ones of the original system. However, it is
proven that the Riemann solutions to the approximated system
converge to the corresponding ones to the original system as the
perturbation parameter tends to zero, which shows that the Riemann
solutions to the nonhomogeneous pressureless Euler equations is stable
under such kind of flux approximation. In a word, we not only
analyze the mechanism of the occurrence of the delta shocks, but
also generalize the result about the stability of Riemann solutions
with respect to flux perturbation from the well-known homogeneous case
to the nonhomogeneous case.
Submitted July 7, 2017. Published May 10, 2019.
Math Subject Classifications: 35L65, 35L67, 35B30.
Key Words: Stability of Riemann solutions; pressureless Euler equations;
delta shock wave; Coulomb-type friction; flux approximation.
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Qingling Zhang School of Mathematics and Computer Sciences Jianghan University Wuhan 430056, China email: zhangqingling2002@163.com |
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