  We investigate a quasilinear initial-boundary value problem for Kuznetsov's
equation with non-homogeneous Dirichlet boundary conditions. This is a model in
nonlinear acoustics which describes the propagation of sound in fluidic media
with applications in medical ultrasound. We prove that there exists a unique
global solution which depends continuously on the sufficiently small data and
that the solution and its temporal derivatives converge at an exponential rate
as time tends to infinity. Compared to the analysis of Kaltenbacher & Lasiecka,
we require optimal regularity conditions on the data and give simplified proofs
which are based on maximal L_p-regularity for parabolic equations and the
implicit function theorem.
