The transport equation is a partial differential equation of the form

(1) |

Here, * u * is a function of two variables *x* and *t*, and the subscripts denote partial derivatives. We will assume that *c* is a fixed constant. Given an initial condition

(2) |

we would like to find a function of two variables that satisfies both the transport equation (1) and the initial condition (2).

This equation can be used to model *pollution* (Lehn and Scherer , undated), *dye dispersion* (Roychoudhury , undated), or even *traffic flow* (Jungel , 2002), with *u* representing the density of the pollutant (or dye or traffic, respectively) at position *x* and time *t*. For a discussion of the physical model, see Knobel (2000). For a discussion of the more general transport equation and its solutions, see Cooper (1998). For discussion and simulation of more general conservation laws, including shock wave phenomena, see Sarra (2003).

**Acknowledgment **

Components for the applet are based on David Eck's Java Components for Mathematics at Hobart and William Smith Colleges.

**About the author**

at University of Michigan-Dearborn .

Published June, 2004

Journal of Online Mathematics and its Applications