Hidden shape derivative in the wave equation with Dirichlet boundary condition |
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| Institution: | CMA, École des mines de Paris - INRIA, 2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis cedex, France;Department of Chemical Engineering and Materials Science, Stevens Institute of Technology, Hoboken 07030, NJ, United States |
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| Abstract: | We establish the shape differentiability for the solution to the wave equation with Dirichlet boundary condition. This is well known for elliptic and parabolic problems. In the hyperbolic situation, the implicit functions theorem does not work, but the hidden regularity (see 5]) gives part of the result. |
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