We analyze the null controllability of a one-dimensional nonlinear system which models the interaction of a fluid and a particle. The fluid is governed by the Burgers equation and the control is exerted on the boundary points. We present two main results: the global null controllability of a linearized system and the local null controllability of the nonlinear original model. The proofs rely on appropriate global Carleman inequalities and fixed point arguments.
On analyse la contrôlabilité nulle d'un système unidimensionnel non linéaire qui modélise l'intéraction d'un fluide et d'une particule. Le fluide est gouverné par l'équation de Burgers et le contrôle est exercé sur la frontière. On présente deux résultats principaux : la contrôlabilité nulle globale d'un système linéarisé et la contrôlabilité nulle locale du système non linéaire originaire. Les démonstrations de ces résultats reposent sur des inégalités de Carleman et des arguments de point fixe appropriés.
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Anna Doubova 1; Enrique Fernández-Cara 1
@article{CRMATH_2003__337_10_657_0, author = {Anna Doubova and Enrique Fern\'andez-Cara}, title = {On the null controllability of a one-dimensional fluid{\textendash}solid interaction model}, journal = {Comptes Rendus. Math\'ematique}, pages = {657--662}, publisher = {Elsevier}, volume = {337}, number = {10}, year = {2003}, doi = {10.1016/j.crma.2003.10.012}, language = {en}, }
TY - JOUR AU - Anna Doubova AU - Enrique Fernández-Cara TI - On the null controllability of a one-dimensional fluid–solid interaction model JO - Comptes Rendus. Mathématique PY - 2003 SP - 657 EP - 662 VL - 337 IS - 10 PB - Elsevier DO - 10.1016/j.crma.2003.10.012 LA - en ID - CRMATH_2003__337_10_657_0 ER -
Anna Doubova; Enrique Fernández-Cara. On the null controllability of a one-dimensional fluid–solid interaction model. Comptes Rendus. Mathématique, Volume 337 (2003) no. 10, pp. 657-662. doi : 10.1016/j.crma.2003.10.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.10.012/
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