In this Note, we present Carleman estimates for linear reaction–diffusion–convection systems of two equations and linear reaction–diffusion systems of three equations. These estimates are the key for proving controllability results for semilinear reaction–diffusion–convection systems of order 2 and reaction–diffusion systems of order 3. They allow us to derive results for identification of n coefficients by observations.
On établit des inégalités d'observabilité pour des systèmes linéaires de réaction–diffusion–convection d'ordre 2 et des systèmes linéaires de réaction–diffusion d'ordre 3, basées sur des estimations de Carleman. Elles permettent de démontrer des résultats de contrôlabilité aux trajectoires par une seule force localisée en espace ainsi que des résultats d'identification de n coefficients par observations.
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Assia Benabdallah 1; Michel Cristofol 1; Patricia Gaitan 1; Luz de Teresa 2
@article{CRMATH_2010__348_1-2_25_0, author = {Assia Benabdallah and Michel Cristofol and Patricia Gaitan and Luz de Teresa}, title = {A new {Carleman} inequality for parabolic systems with a single observation and applications}, journal = {Comptes Rendus. Math\'ematique}, pages = {25--29}, publisher = {Elsevier}, volume = {348}, number = {1-2}, year = {2010}, doi = {10.1016/j.crma.2009.11.001}, language = {en}, }
TY - JOUR AU - Assia Benabdallah AU - Michel Cristofol AU - Patricia Gaitan AU - Luz de Teresa TI - A new Carleman inequality for parabolic systems with a single observation and applications JO - Comptes Rendus. Mathématique PY - 2010 SP - 25 EP - 29 VL - 348 IS - 1-2 PB - Elsevier DO - 10.1016/j.crma.2009.11.001 LA - en ID - CRMATH_2010__348_1-2_25_0 ER -
%0 Journal Article %A Assia Benabdallah %A Michel Cristofol %A Patricia Gaitan %A Luz de Teresa %T A new Carleman inequality for parabolic systems with a single observation and applications %J Comptes Rendus. Mathématique %D 2010 %P 25-29 %V 348 %N 1-2 %I Elsevier %R 10.1016/j.crma.2009.11.001 %G en %F CRMATH_2010__348_1-2_25_0
Assia Benabdallah; Michel Cristofol; Patricia Gaitan; Luz de Teresa. A new Carleman inequality for parabolic systems with a single observation and applications. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 25-29. doi : 10.1016/j.crma.2009.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.001/
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