2.3.6 Integral form and weak solution
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
):
(95)
Definition:
Weak solution
of PDE in differential form: solution of PDE in integral form
.
In smooth regions: weak solution = solution.