  In thermoacoustic and photoacoustic tomography an electromagnetic wave is
sent through a medium, heating it and therefore generating an elastic expansion
that in turns generates an acoustic wave that is measured outside the medium.
The general problem is to recover both the inhomogeneous sound speed and the
initial pressure from the boundary measurements of the solution of the acoustic
wave equation with a single measurement of the pressure. We show that one can
recover both the sound speed and the initial pressure assuming a monocitiy
condition on the sound speed that includes the physically interesting case of
piecewise constant sound speeds. We also establish a link between this problem
and the corresponding transmission eigenvalue problem.
