# American Institute of Mathematical Sciences

September  2016, 5(3): 399-430. doi: 10.3934/eect.2016011

## The shape derivative for an optimization problem in lithotripsy

 1 Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt 2 University of Graz, Heinrichstraße 36, 8010 Graz, Austria

Received  January 2016 Revised  March 2016 Published  August 2016

In this paper we consider a shape optimization problem motivated by the use of high intensity focused ultrasound in lithotripsy. This leads to the problem of designing a Neumann boudary part in the context of the Westervelt equation, which is a common model in nonlinear acoustics. Based on regularity results for solutions of this equation and its linearization, we rigorously compute the shape derivative for this problem, relying on the variational framework from [9].
Citation: Barbara Kaltenbacher, Gunther Peichl. The shape derivative for an optimization problem in lithotripsy. Evolution Equations & Control Theory, 2016, 5 (3) : 399-430. doi: 10.3934/eect.2016011
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