[Contrôlabilité frontière à zéro des équations linéaires de type diffusion–réaction]
Il s'agit de la contrôlabilité frontière à zéro des équations linéaires de type diffusion–réaction dans un domaine borné de
This Note deals with the boundary null-controllability of linear diffusion–reaction equations in a 2D bounded domain. We transform the determination of the sought HUM boundary control into the minimization of a continuous and strictly convex functional. In the case of a rectangular domain where the diffusion tensor is represented by a diagonal matrix, we establish a procedure based on the inner product method that uses a complete orthonormal family of Sturm–Liouville's eigenfunctions to express explicitly the sought control.
Accepté le :
Publié le :
Adel Hamdi 1 ; Imed Mahfoudhi 1
@article{CRMATH_2010__348_19-20_1083_0, author = {Adel Hamdi and Imed Mahfoudhi}, title = {Boundary null-controllability of linear diffusion{\textendash}reaction equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {1083--1086}, publisher = {Elsevier}, volume = {348}, number = {19-20}, year = {2010}, doi = {10.1016/j.crma.2010.09.019}, language = {en}, }
Adel Hamdi; Imed Mahfoudhi. Boundary null-controllability of linear diffusion–reaction equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1083-1086. doi : 10.1016/j.crma.2010.09.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.019/
[1] Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Research Institute of Math., Global Anal. Research Center, Seoul National University, 1996
[2] A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods, Japan J. Appl. Math., Volume 7 (1990), pp. 1-76
[3] The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution, Inverse Problems, Volume 25 (2009) no. 7, pp. 75006-75023
[4] Identification of point sources in two-dimensional advection–diffusion–reaction equation: application to pollution sources in a river: Stationary case, Inverse Probl. Sci. Eng., Volume 15 (2007) no. 8, pp. 855-870
[5] Null-controllability of a system of linear thermoelasticity, Arch. Ration. Mech. Anal., Volume 141 (1998), pp. 297-329
[6] Contrôlabilité Exacte Pertubations et Stabilisation de Systèmes Distribués, Tome 1: Contrôlabilité Exacte, Recherches en Mathématiques Appliquées, vol. 8, Masson, Paris, 1988
[7] Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., Volume 30 (1988) no. 1, pp. 1-68
[8] Contrôlabilité frontière des équations linéaires de type diffusion–réaction, Mémoire de recherche, LMI-INSA de Rouen, France, 2010
[9] Uniform boundary controllability of a discrete 1-D wave equation, Systems Control Lett., Volume 48 (2003) no. 3–4, pp. 261-280
[10] J.M. Rasmussen, Boundary control of linear evolution PDEs—continuous and discrete, PhD Thesis, Technical University of Denmark, 2004.
[11] Partial Differential Equations, Springer, 1991
[12] Basic Linear Partial Differential Equations, Academic Press, 1975
Cité par Sources :
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier