Regional Boundary Exact Controllability of the Wave Equation by Strategic Actuators on a Polygonal Domain with Cracks
Cheikh Seck *
Département de Mathématiques de la FASTEF ex ENS de l'Université Cheikh Anta Diop de Dakar, Sénégal and Laboratoire d'Analyse Numérique et d'Informatique (LANI) de l'UFR SAT , BP 234, Université Gaston Berger, Saint-Louis, Sénégal.
Ousmane Sène
Département de mathématiques et d'Informatique de la Faculté des Sciences et Techniques de l'Université Cheikh Anta Diop de Dakar, Sénégal.
Teuw Niane
Laboratoire d'Analyse Numérique et d'Informatique (LANI) de l'UFR SAT , BP 234, Université Gaston Berger, Saint-Louis, Sénégal.
*Author to whom correspondence should be addressed.
Abstract
In this work we prove the exact controllability of the wave equation by acting on a strategic zone of the border of a non-convex polygonal domain with crack. Indeed, by combining two methods: that of Grisvard on the exact controllability on domains with corners and that of EL. Jai on the boundary strategic actutors, this exact controllability result has been proven.
Keywords: Laplacian, singularities, dualities, cracks, controllability, error estimations, strategic actuators