IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3103-d1193556.html
   My bibliography  Save this article

Weak and Classical Solutions to Multispecies Advection–Dispersion Equations in Multilayer Porous Media

Author

Listed:
  • Miglena N. Koleva

    (Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, Bulgaria)

  • Lubin G. Vulkov

    (Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, Bulgaria)

Abstract

The basic model motivating this work is that of contaminant transport in the Earth’s subsurface, which contains layers in which analytical and semi-analytical solutions of the corresponding advection–dispersion equations could be derived. Then, using the interface relations between adjacent layers, one can streamline the study of the model to the solution to the initial boundary value problem for a coupled parabolic system on partitioned domains. For IBVPs, we set up weak formulations and prove the existence and uniqueness of solutions to appropriate Sobolev-like spaces. A priori estimates at different levels of input data smoothness were obtained. The nonnegativity preservation over time of the solution is discussed. We numerically demonstrate how to solve the reduced truncated problem instead of the original multispecies one with a large number of layers.

Suggested Citation

  • Miglena N. Koleva & Lubin G. Vulkov, 2023. "Weak and Classical Solutions to Multispecies Advection–Dispersion Equations in Multilayer Porous Media," Mathematics, MDPI, vol. 11(14), pages 1-18, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3103-:d:1193556
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3103/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/14/3103/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abhishek Sanskrityayn & Heejun Suk & Jui-Sheng Chen & Eungyu Park, 2021. "Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients," Sustainability, MDPI, vol. 13(14), pages 1-23, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:gam:jmathe:v:11:y:2023:i:14:p:3103-:d:1193556. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      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.