Electron. J. Differential Equations,
Vol. 2019 (2019), No. 65, pp. 122.
Stability of Riemann solutions to pressureless Euler equations with
Coulombtype friction by flux approximation
Qingling Zhang
Abstract:
We study the stability of Riemann solutions to pressureless Euler
equations with Coulombtype friction under the nonlinear
approximation of flux functions with one parameter. The approximated
system can be seen as the generalized Chaplygin pressure AwRascle
model with Coulombtype friction, which is also equivalent to the
nonsymmetric system of KeyfitzKranzer type with generalized
Chaplygin pressure and Coulombtype 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 wellknown 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; Coulombtype 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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