Transport Equation
Jan 1, 2021
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1 min read
Summary
This lecture introduces the transport equation
$$ u_t + b\cdot Du = 0,\quad \text{in}~ \mathbb{R}^n\times\mathbb{R} $$and gives a procedure based on (a very basic) implementation of the method of characteristics for the solution of the initial-value problem
$$ \left\{ \begin{alignedat}{2} u_t + b\cdot Du &= 0\quad &&\text{in}~ \mathbb{R}^n\times\mathbb{R}\\\ u&=g\quad &&\text{on}~ \mathbb{R}^n \end{alignedat} \right. $$for an unknown function $u=u(x,t)$, $u \colon \mathbb{R}^n\times\mathbb{R} \to \mathbb{R}$ and a given function $g\colon \mathbb{R}^n\to \mathbb{R}$ with sufficient regularity.
Full Set of Lecture Notes
The notes for this lecture are available here (14 pages).
