  In this paper, we pursue our series of papers aiming to show the
applicability of the concept of very weak solutions. We consider a wave model
with irregular position dependent mass and dissipation terms, in particular,
allowing for delta-like coefficients and prove that the problem has a very weak
solution. Furthermore, we prove the uniqueness in an appropriate sense and the
coherence of the very weak solution concept with classical theory. A special
case of the model considered here, is the so-called telegraph equation.
