Abstract
When the property of interest in a system depends on secondary independent variables (such as spatial position, particle speed, particle size) then its evolution can be described by a partial differential equation (PDE). In the context of properties depending on space and time, such PDEs are called transport equations, and they are generally written as first order evolution equations. We overview the formulation of transport equations and their relationship to conservation laws. We also summarise solution techniques based on travelling wave solutions and the method of characteristics.
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Notes
- 1.
Assuming the integrand to be a smooth function.
- 2.
See Fig. 2.4—the placement of the shock not only conserves the area of the newly-formed right triangle, but also requires that the areas of the two cut-off multi-valued regions from the obtuse triangle to be equal.
- 3.
A wave being specified by a boundary condition from a fixed “signal source” position.
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© 2015 Springer International Publishing Switzerland
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Witelski, T., Bowen, M. (2015). Transport Equations. In: Methods of Mathematical Modelling. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23042-9_2
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DOI: https://doi.org/10.1007/978-3-319-23042-9_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23041-2
Online ISBN: 978-3-319-23042-9
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