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We investigate the Westervelt equation from nonlinear acoustics, subject tononlinear absorbing boundary conditions of order zero, which were recentlyproposed by Kaltenbacher & Shevchenko. We apply the concept of maximalregularity of type $L_p$ to prove global well-posedness for small initial data.Moreover, we show that the solutions regularize instantaneously which meansthat they are $C^\infty$ with respect to time $t$ as soon as $t>0$. Finally, weshow that each equilibrium is stable and each solution which startssufficiently close to an equilibrium converges at an exponential rate to apossibly different equilibrium.

Well-posedness and long-time behavior for the Westervelt equation with absorbing boundary conditions of order zero