Transport equation
Also known as advection equation and first order linear wave equation. Related: wave equation.
It is the simplest PDE exhibiting travelling wave solutions (it is said in this video. We want a function $u(x,t)$
$$ u_t+cu_x=0 $$with $c\in\mathbb{R}$.
In the video it is said that the characteristics lines are those curves in space $(x,t)$ such that $u$ is constant along them: $u(\gamma(t))=cte$. That is, the red lines below:
This is probably related to similarity solutions and to the method of characteristics.
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Author of the notes: Antonio J. Pan-Collantes
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