  The paper studies the possible blowup of the total variation for entropy weak
solutions of the p-system, modeling isentropic gas dynamics. It is assumed that
the density remains uniformly positive, while the initial data can have
arbitrarily large total variation (measured in terms of Riemann invariants).
Two main results are proved. (I) If the total variation blows up in finite
time, then the solution must contain an infinite number of large shocks in a
neighborhood of some point in the $t$-$x$ plane. (II) Piecewise smooth
approximate solutions can be constructed whose total variation blows up in
finite time. For these solutions the strength of waves emerging from each
interaction is exact, while rarefaction waves satisfy the natural decay
estimates stemming from the assumption of genuine nonlinearity.
