%0 Journal Article %T Absorbing boundary conditions for the Westervelt equation %A Barbara Kaltenbacher %A Igor Shevchenko %J Mathematics %D 2014 %I arXiv %X 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. %U http://arxiv.org/abs/1408.5031v1