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arXiv · 1603.02097

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

Gieri Simonett·Mathias Wilke
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Abstract

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

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Gieri Simonett, Mathias Wilke. 2016-03-07. Well-posedness and long-time behavior for the Westervelt equation with absorbing boundary conditions of order zero. https://arxiv.org/abs/1603.02097

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