IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v82y2011i4p679-690.html
   My bibliography  Save this article

On the linear advection equation subject to random velocity fields

Author

Listed:
  • Dorini, F.A.
  • Cunha, M.C.C.

Abstract

This paper deals with the random linear advection equation for which the time-dependent velocity and the initial condition are independent random functions. Expressions for the density and joint density functions of the solution are given. We also verify that in the Gaussian time-dependent velocity case the probability density function of the solution satisfies a convection–diffusion equation with a time-dependent diffusion coefficient. Some exact examples are presented.

Suggested Citation

  • Dorini, F.A. & Cunha, M.C.C., 2011. "On the linear advection equation subject to random velocity fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 679-690.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:4:p:679-690
    DOI: 10.1016/j.matcom.2011.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847541100259X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2011.10.008?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.

    References listed on IDEAS

    as
    1. Cunha, M. Cristina C. & Dorini, Fábio A., 2009. "Statistical moments of the solution of the random Burgers–Riemann problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1440-1451.
    2. Cortés, J.C. & Jódar, L. & Villafuerte, L., 2009. "Random linear-quadratic mathematical models: Computing explicit solutions and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2076-2090.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Calatayud, J. & Cortés, J.-C. & Jornet, M., 2018. "The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 261-279.
    2. Calatayud, Julia & Carlos Cortés, Juan & Jornet, Marc, 2020. "Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Shalimova Irina & Sabelfeld Karl K., 2019. "A random walk on small spheres method for solving transient anisotropic diffusion problems," Monte Carlo Methods and Applications, De Gruyter, vol. 25(3), pages 271-282, September.
    4. Bevia, V. & Burgos, C. & Cortés, J.-C. & Navarro-Quiles, A. & Villanueva, R.-J., 2020. "Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Calatayud, J. & Cortés, J.-C. & Dorini, F.A. & Jornet, M., 2020. "Extending the study on the linear advection equation subject to stochastic velocity field and initial condition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 159-174.

    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.
    1. Bevia, V. & Burgos, C. & Cortés, J.-C. & Navarro-Quiles, A. & Villanueva, R.-J., 2020. "Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Conceição, D. & Lambert, W., 2015. "Statistical moments for solutions of non-linear scalar equations with random Riemann data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 120-133.
    3. Cortés, J.-C. & Moscardó-García, A. & Villanueva, R.-J., 2022. "Uncertainty quantification for hybrid random logistic models with harvesting via density functions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Arenas, Abraham J. & González-Parra, Gilberto & Jódar, Lucas, 2010. "Randomness in a mathematical model for the transmission of respiratory syncytial virus (RSV)," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 971-981.

    More about this item

    Keywords

    35R60; 60H15; Advection; Random; Velocity; Gaussian processes;
    All these keywords.

    JEL classification:

    Statistics

    Access and download statistics

    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:82:y:2011:i:4:p:679-690. 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: 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.