%0 Journal Article
%T Smooth and discontinuous junctions in the p-system
%A Rinaldo M. Colombo
%A Francesca Marcellini
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0909.1980v1