  The paper introduces a new way to construct dissipative solutions to a second
order variational wave equation. By a variable transformation, from the
nonlinear PDE one obtains a semilinear hyperbolic system with sources. In
contrast with the conservative case, here the source terms are discontinuous
and the discontinuities are not always crossed transversally. Solutions to the
semilinear system are obtained by an approximation argument, relying on
Kolmogorov's compactness theorem. Reverting to the original variables, one
recovers a solution to the nonlinear wave equation where the total energy is a
monotone decreasing function of time.
