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On the linear advection equation subject to random velocity fields

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    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. 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.
    3. 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).
    4. 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.
    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.

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    More about this item

    Keywords

    35R60; 60H15; Advection; Random; Velocity; Gaussian processes;
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