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The shape derivative for an optimization problem in lithotripsy

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  • 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].
    Mathematics Subject Classification: Primary: 49Q10, 35L72; Secondary: 35L80, 49K20.


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