  The Blackstock-Crighton equation models nonlinear acoustic wave propagation
in thermo-viscous fluids. In the present work we investigate the associated
inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain
and prove long-time well-posedness and exponential stability for sufficiently
small data. The solution depends analytically on the data. In the Dirichlet
case, the solution decays to zero and the same holds for Neumann conditions if
the data have zero mean.
  We choose an optimal $L_p$-setting, where the regularity of the initial and
boundary data are necessary and sufficient for existence, uniqueness and
regularity of the solution. The linearized model with homogeneous boundary
conditions is represented as an abstract evolution equation for which we show
maximal $L_p$-regularity. In order to eliminate inhomogeneous boundary
conditions, we establish a general higher regularity result for the heat
equation. We conclude that the linearized model induces a topological linear
isomorphism and then solve the nonlinear problem by means of the implicit
function theorem.
