  The Blackstock-Crighton equations describe the motion of a viscous,
heat-conducting, compressible fluid. They are used as models for acoustic wave
propagation in a medium in which both nonlinear and dissipative effects are
taken into account. In this article, a mathematical analysis of the
Blackstock-Crighton equations with a time-periodic forcing term is carried out.
For arbitrary time-periodic data (sufficiently restricted in size) it is shown
that a time-periodic solution of the same period always exists. This implies
that the dissipative effects are sufficient to avoid resonance within the
Blackstock-Crighton models. The equations are considered in a three-dimensional
bounded domain with both non-homogeneous Dirichlet and Neumann boundary values.
Existence of a solution is obtained via a fixed-point argument based on
appropriate a priori estimates for the linearized equations.
