I'm studying the transport equation
$$u_t + cu_x = 0$$
Where c is a constant.
What does the solution, $u(x,t)$, describe? Is it ... the height of the wave? The location of the wave? Does the transport equation only describe waves?
The source that I am studying from only says, "the wave, u(x,t) ... "
I know in the heat equation, the solution $u$ is temperature (dependent on position x and time t) and in the wave equation, the solution $u$ gives the height of the wave.
So, I'm just not sure of what the solution to the transport equation describes.