  Consider the p-system describing the subsonic flow of a fluid in a pipe with
section a = a(x). We prove that the resulting Cauchy problem generates a
Lipschitz semigroup, provided the total variation of the initial datum and the
oscillation of a are small. An explicit estimate on the bound of the total
variation of a is provided, showing that at lower fluid speeds, higher total
variations of a are acceptable. An example shows that the bound on TV(a) is
mandatory, for otherwise the total variation of the solution may grow
arbitrarily.
