Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 15 de enero de 2014
Hora  : 10:30
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

Arnaud Munch

(Université Blaise Pascal, Clermont-Ferrand, Francia)

Resumen

This talk deals with the numerical computation of distributed null controls for the 1D wave equation. We consider supports of the controls that may vary with respect to the time variable. The goal is to compute approximations of such controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. Under specific geometric conditions on the support of the controls earlier introduced in [Castro, Exact controllability of the 1-D wave equation from a moving interior point, 2013], we first prove a generalized observability inequality for the homogeneous wave equation. We then introduce and prove the well-posedness of a mixed formulation that characterizes the controls of minimal square-integrable norm. Such mixed formulation, introduced in [Cindea and M\"unch, A mixed formulation for the direct approximation of the control of minimal square integrable norm for linear type wave equations], and solved in the framework of the (space-time) finite element method, is particularly well-adapted to address the case of time dependent support. Several numerical experiments are discussed. This work is in collaboration with Carlos Castro (Universidad politecnica de Madrid) and Nicolae Cindea (Univ. Blaise Pascal, Clermont-Ferrand).

Geometrical illustration