Transport equation

Summary

The transport equation $u_t + b \cdot \nabla u = 0$ says that a quantity $u$ is carried along by a flow of velocity $b$ without changing. It is the simplest first-order partial differential equation, also called the advection equation. Its solutions are the initial profile moved along the flow. It is the model problem for the method of characteristics and for numerical schemes of hyperbolic equations. See the definition.