- Any solution of the advection equation
in differential form (63)
has to have derivatives.
- However, any function - even a discontinuous one - can be propagated along characteristics
(Sect. 2.1.5).
Transformation: linear advection equation in
integral form
(see Fig. 5 and Sect. 1.2.5):
![\begin{displaymath}
\int_{x_0}^{x_1}
\left[ \rho \! \left( x , t_1 \right)
-
...
... \right)
-
\rho \! \left( x_0 , t \right)
\right]
dt
=
0
\end{displaymath}](img200.png) |
(95) |
Definition:
Weak solution
of PDE in differential form:
solution of
PDE in integral form.
In smooth regions: weak solution = solution.