The shape derivative for an optimization problem in lithotripsy

DOI10.3934/eect.2016011zbMath1350.49064OpenAlexW2518089922MaRDI QIDQ330419

Barbara Kaltenbacher, Gunther H. Peichl

Publication date: 26 October 2016

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/eect.2016011

zbMATH Keywords

well-posednessnonlinear acousticsshape optimizationpartial differential equationslithotripsy

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Optimization of shapes other than minimal surfaces (49Q10) Degenerate hyperbolic equations (35L80) Second-order quasilinear hyperbolic equations (35L72)

Related Items (4)

Analysis of general shape optimization problems in nonlinear acoustics ⋮ Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy ⋮ A Priori Error Estimates for the Finite Element Approximation of Westervelt's Quasi-linear Acoustic Wave Equation ⋮ Isogeometric shape optimization for nonlinear ultrasound focusing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Dirichlet-Neumann cost functional approach for the Bernoulli problem
• Boundary optimal control of the Westervelt and the Kuznetsov equations
• Absorbing boundary conditions for nonlinear acoustics: the Westervelt equation
• Avoiding degeneracy in the Westervelt equation by state constrained optimal control
• Shapes and Geometries
• Variational approach to shape derivatives
• Theoretical Numerical Analysis

This page was built for publication: The shape derivative for an optimization problem in lithotripsy