The Multiple Scale Transport Equation in One Space Dimension

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Mathematics (HMC)

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This study examines the behavior of the one-dimensional non-homogeneous transport equation of the form εut= ux+f, ε<<1. The solution consists of behavior which changes on two different time scales, one rapid and one slow. This time scale behavior is known. Additionally, however, we find here that because of the presence of the non-homogeneous forcing term f, and large wave speed 1/ε, there is a component of the solution which will vary only on a very large spatial scale. This large space-scale solution persists throughout all time, even after the source term of the solution has been shut off. The analysis of this large spacescale behavior is the focus of this paper. Numerical experiments highlight some of our results. These results have applications in fields such as meteorology, and other areas where multiple time scales are of interest.

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© 1998 Springer Verlag