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Wave Interactions and Stability of Riemann Solutions to the Aw-Rascle Model with Friction for Modified Chaplygin Gas

Wave Interactions and Stability of Riemann Solutions to the Aw-Rascle Model with Friction for... We study wave interactions and stability of Riemann solutions to the inhomogeneous Aw-Rascle (AR) model with Coulomb-like friction term for modified Chaplygin gas. First, the Riemann problem with initial data of two piecewise constants is technically solved by introducing some variable transformation. It is found that the Riemann solutions for the inhomogeneous system are no longer self-similar, and all the elementary waves are bent into parabolic shapes. Second, by investigating the interactions of elementary waves, the global structures of Riemann solutions to the inhomogeneous AR model with perturbed three-piecewise-constant initial data are established constructively. Moreover, we show that the solutions are stable under the small perturbation of initial data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Bulletin of the Brazilian Mathematical Society, New Series" Springer Journals

Wave Interactions and Stability of Riemann Solutions to the Aw-Rascle Model with Friction for Modified Chaplygin Gas

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Publisher
Springer Journals
Copyright
Copyright © Sociedade Brasileira de Matemática 2021
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-021-00282-5
Publisher site
See Article on Publisher Site

Abstract

We study wave interactions and stability of Riemann solutions to the inhomogeneous Aw-Rascle (AR) model with Coulomb-like friction term for modified Chaplygin gas. First, the Riemann problem with initial data of two piecewise constants is technically solved by introducing some variable transformation. It is found that the Riemann solutions for the inhomogeneous system are no longer self-similar, and all the elementary waves are bent into parabolic shapes. Second, by investigating the interactions of elementary waves, the global structures of Riemann solutions to the inhomogeneous AR model with perturbed three-piecewise-constant initial data are established constructively. Moreover, we show that the solutions are stable under the small perturbation of initial data.

Journal

"Bulletin of the Brazilian Mathematical Society, New Series"Springer Journals

Published: Jan 15, 2022

Keywords: Aw-Rascle model; Friction term; Riemann problem; Wave interactions; Modified Chaplygin gas

References