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The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model
  • Yunfeng Zhang,
  • Meina Sun
Yunfeng Zhang
Ludong University
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Meina Sun
Ludong University
Author Profile

Abstract

The exact solutions of the Riemann problems for the two different perturbed macroscopic production models are considered and constructed respectively for all the possible cases. It is found that the asymptotic limits of solutions to the Riemann problem for the first kind of perturbed macroscopic production model do not coverage to those of the pressureless gas dynamics model, because the delta shock wave in the limiting situation has different propagation speed and strength from those for the pressureless gas dynamics model. In order to remedy it, the second kind of perturbed macroscopic production model is proposed, whose asymptotic limits of Riemann solutions are identical with those of the pressureless gas dynamics model.

Peer review status:UNDER REVIEW

25 Jan 2021Submitted to Mathematical Methods in the Applied Sciences
26 Jan 2021Submission Checks Completed
26 Jan 2021Assigned to Editor
31 Jan 2021Reviewer(s) Assigned
11 May 2021Review(s) Completed, Editorial Evaluation Pending
12 May 2021Editorial Decision: Revise Minor
20 May 20211st Revision Received
20 May 2021Submission Checks Completed
20 May 2021Assigned to Editor
20 May 2021Reviewer(s) Assigned