Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 416, Issue 2, Pages 839-854Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.03.010
Keywords
Aw-Rascle model; Chaplygin gas; Modified Chaplygin gas; Delta-shocks; Numerical simulations
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Funding
- National Natural Science Foundation of China [11361073, 11226191]
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This paper studies the limit of solutions to the Aw-Ftascle model as the pressure tends to the Chaplygin gas pressure. For concreteness, the pressure is taken as a modified Chaplygin gas pressure. Firstly, the Riemann problem for the Aw-Rascle model with the modified Chaplygin gas pressure is solved constructively. Secondly, it is shown that as the pressure tends to the Chaplygin gas pressure, some Riemann solutions containing a shock and a contact discontinuity tend to a delta-shock solution, whose propagation speed and strength are different from those of deltashock solution to the Aw-Rascle model with a Chaplygin gas pressure. Besides, it is also proven that the rest Riemann solutions converge to a two-contact-discontinuity solution, which is exactly the solution to the Aw-Rascle model with a Chaplygin gas pressure. Thirdly, some numerical results are presented to exhibit the process of formation of delta-shocks. (C) 2014 Elsevier Inc. All rights reserved.
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