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| This talk will provide a full analysis of shape differentiability for the solution to the second order hyperbolic equation with Neumann boundary conditions. This answers a fundamental question in shape optimization and control problems for the linear wave equations and coupled systems where the hyperbolic equation is coupled with other dynamics, and the matching conditions at the boundary are of Neumann type. While the shape derivative analysis has been solved for many classical linear problems, the hyperbolic situation is more delicate, due to the lack of good boundary regularity for the wave solution, which is a key ingredient in the differentiability analysis. Therefore the talk will also include a new hidden regularity result, obtained through a new pseudo-extractor technique. |
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