  The Cauchy-Dirichlet problem for the Moore-Gibson-Thompson equation is
analyzed. With the focus on non-homogeneous boundary data, two approaches are
offered: one is based on the theory of hyperbolic equations, while the other
one uses the theory of operator semigroups. This is a mixed hyperbolic problem
with a characteristic spatial boundary. Hence, the regularity results exhibit
some deficiencies when compared with the non-characteristic case.
