next up previous contents index

1.5.2 Quasi-linear system

In Eq. (41) we can compute the spatial derivative and get

\;\! \frac{\partial }{\partial t} \ensuremath{\mathchoice{\...$\scriptstyle 0$}}
{\mbox{\boldmath$\scriptscriptstyle 0$}}}
\end{displaymath} (43)
with the Jacobian
\bar{\bar{\ensuremath{\mathsf{A}}}} = \frac{\partial \ensur...
...e q$}}
{\mbox{\boldmath$\scriptscriptstyle q$}}}}
\enspace .
\end{displaymath} (44)
A system of partial differential equations in the form of Eq. (43) is called quasi-linear if
\bar{\bar{\ensuremath{\mathsf{A}}}} = \bar{\bar{\ensuremath...
...x{\boldmath$\scriptscriptstyle q$}}}, x, t \right)
\enspace .
\end{displaymath} (45)

It is linear if \bgroup\color{DEFcolor}$\bar{\bar{\ensuremath{\mathsf{A}}}}$\egroup is constant.