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We study the Jordan--Moore--Gibson--Thompson (JMGT) equation, a third orderin time wave equation that models nonlinear sound propagation, in thepractically relevant setting of Neumann and absorbing boundary conditions. Inthe analysis, we pay special attention to dependencies on the coefficient$\tau$ of the third order time derivative that plays the physical role ofrelaxation time. We establish local in time well-posedness and derive energybounds 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 aclassical model in nonlinear acoustics, the Westervelt equation, as singularlimits of solutions to the JMGT equation.

Vanishing relaxation time limit of the Jordan--Moore--Gibson--Thompson wave equation with Neumann and absorbing boundary conditions