Method of Characteristics: Local Theory
Summary
We continue the general treatment of the method of characteristics Lecture 15 to construct solutions of the Cauchy problem $$ \left\{ \begin{alignedat}{2} F(Du,u,x) &= 0 &&\text{in}~U \\ u&=g\quad &&\text{on}~\Gamma \end{alignedat} \right. $$ We cover
- the non-characteristic condition
- compatibility conditions
for the boundary curve $\Gamma$ and data.
We then move on to the local theory.