Original articles: On the linear advection equation subject to random velocity fields

Authors:
F. A. Dorini;M. C. C. Cunha
Affiliations:
Department of Mathematics, Federal University of Technology - Paraná, 80230-901, Curitiba, PR, Brazil;Department of Applied Mathematics, State University of Campinas, 13083-970, Campinas, SP, Brazil
Venue:
Mathematics and Computers in Simulation
Year:
2011

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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.