  We study the Jordan--Moore--Gibson--Thompson (JMGT) equation, a third order
in time wave equation that models nonlinear sound propagation, in the
practically relevant setting of Neumann and absorbing boundary conditions. In
the analysis, we pay special attention to dependencies on the coefficient
$\tau$ of the third order time derivative that plays the physical role of
relaxation time. We establish local in time well-posedness and derive energy
bounds that can be made independent of $\tau$ under appropriate conditions.
This fact allows us to pass to the limit $\tau\to0$ and recover solutions of a
classical model in nonlinear acoustics, the Westervelt equation, as singular
limits of solutions to the JMGT equation.
