# American Institute of Mathematical Sciences

2015, 2015(special): 1000-1008. doi: 10.3934/proc.2015.1000

## Absorbing boundary conditions for the Westervelt equation

 1 Imperial College London, Department of Mathematics, London, SW7 2AZ, United Kingdom 2 Alpen-Adria-Universität Klagenfurt, Institute of Mathematics, Klagenfurt, A-9020, Austria

Received  September 2014 Revised  December 2014 Published  November 2015

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation.
Citation: Igor Shevchenko, Barbara Kaltenbacher. Absorbing boundary conditions for the Westervelt equation. Conference Publications, 2015, 2015 (special) : 1000-1008. doi: 10.3934/proc.2015.1000
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