IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v234y2025icp15-30.html
   My bibliography  Save this article

The singular wave in a pressureless hydrodynamic model

Author

Listed:
  • Wei, Zhijian
  • Guo, Lihui

Abstract

In this paper, we investigate the non-classical wave for a pressureless hydrodynamic model with the flux perturbed term by the Riemann problem and a singularity formation. All the possible Riemann solutions, the combination of two contact discontinuities J1+J2, and a delta shock wave δS, are constructed in fully explicit forms. It should be mentioned that the delta shock wave appears in the solution if and only if the flux perturbed parameter ɛ satisfies some specific condition. Due to the particularity of the delta shock wave in the Riemann solutions, we investigate the formation of singularity, namely, the traffic density blowing up under certain data. Moreover, its result gives an example of the conjecture proposed by Majda [Springer New York, 1984]: “If a hyperbolic system of conservation laws is totally linearly degenerate, then the system has smooth global solutions when the initial data are smooth, unless the solution itself blows up in a finite time.” We further explore and discuss their asymptotic behaviors to analyze the effect of ɛ, in which the delta shock wave and vacuum state solutions for a pressureless hydrodynamic model can be obtained by J1+J2 as ɛ tends to 0. In addition, we offer some typical numerical simulations that are identical well to our theoretical results and provide a more intuitive way to observe the singular wave.

Suggested Citation

  • Wei, Zhijian & Guo, Lihui, 2025. "The singular wave in a pressureless hydrodynamic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 15-30.
    • Handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:15-30
    DOI: 10.1016/j.matcom.2025.02.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425000540
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.02.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:15-30. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.