Optimal location of the support of the control for the 1-D wave equation: numerical investigations

摘要: We consider in this paper the homogeneous 1-D wave equation defined on ???. Using Hilbert Uniqueness Method, one may define, for each subset ???, exact control v ? of minimal L 2(?×(0,T))-norm which drives to rest system at a time T>0 large enough. address question optimal position minimizes functional $J:\omega \rightarrow \|v_{\omega}\|_{L^{2}(\omega \times (0,T))}$ . express shape derivative J as an integral ?×(0,T) independently any adjoint solution. This expression leads descent direction and permits define gradient algorithm efficiently initialized by topological associated with J. The numerical approximation problem is discussed experiments are presented framework level set approach. also investigate well-posedness considering relaxed formulation.