Contrôlabilité exacte des solutions de l’équation des ondes en présence de singularités. (Exact controllability of solutions to the wave equation under presence of singularities). (French) Zbl 0683.49012

Grisvard, P.

J. Math. Pures Appl., IX. Sér. 68, No. 2, 215-259 (1989).

Summary: This is an adaptation of the Hilbert uniqueness method worked out by J. L. Lions [Exact controllability, stabilization and perturbation for distributed systems, Von Neumann lecture, SIAM meeting, Boston/July 1986; see also SIAM Rev. 30, No.1, 1-68 (1988; Zbl 0644.49028)] in domains with regular boundaries to the case when the domain has a polygonal or a polyhedral boundary and to the case of mixed boundary conditions i.e. when singular solutions occur. One is led to impose some restrictions of geometrical character to the domain under consideration. This is in order to get the minimum amount of regularity for the solution of the wave equation that will allow one to perform the integrations by parts of the multiplier method. The main difficulties come from fractures on the one hand and from the mixed Dirichlet-Neumann conditions on the other hand (even when the boundary is regular).

MSC:

93B03	Attainable sets, reachability
35L05	Wave equation
93B05	Controllability

Keywords:

Hilbert uniqueness method; singular solutions; wave equation; fractures; mixed Dirichlet-Neumann conditions

Citations:

Zbl 0644.49028