Shape Sensitivity Analysis in Hyperbolic Problems with Nonsmooth Domains
2001
The control with respect to the domain is inherently not linear due to the non linear structure of the set of domains. In this paper we investigate the sensitivity of the solution of an hyperbolic PDE with respect to the domain. This analysis is carried out with the wave equation with an homogeneous Dirichlet boundary condition. The novelty lies in the absence of regularity of the domain with respect to which the analysis is done. In a sense we extend the result presented in [6] to the case of Lipschitz-continuous domains.