Artículo
Observability inequalities on measurable sets for the stokes system and applications
Autor/es | Chaves Silva, Felipe Wallison
Araujo de Souza, Diego Zhang, Can |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2020-07-29 |
Fecha de depósito | 2023-04-25 |
Publicado en |
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Resumen | In this paper, we establish spectral inequalities on measurable sets of positiveLebesgue measure for the Stokes operator, as well as observability inequalities on space-time mea-surable sets of positive ... In this paper, we establish spectral inequalities on measurable sets of positiveLebesgue measure for the Stokes operator, as well as observability inequalities on space-time mea-surable sets of positive measure for nonstationary Stokes system. The latter extends the resultestablished recently by Wang and Zhang [SIAM J. Control Optim.,55 (2017), pp. 1862--1886] to thecase of observations from subsets of positive measure in both time and space variables. Furthermore,we present their applications in the shape optimization problem, as well as the time optimal controlproblem for the Stokes system. In particular, we give a positive answer to an open question raisedby Privat, Tr\'elat, and Zuazua [Arch. Rational Mech. Anal.,216 (2015), pp. 921--981]. |
Cita | Chaves Silva, F.W., Araujo de Souza, D. y Zhang, C. (2020). Observability inequalities on measurable sets for the stokes system and applications. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58 (4), 2188-2205. https://doi.org/10.1137/18M117652X. |
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