Artículo
Minimal time for the null controllability of parabolic systems: the effect of the condensation index of complex sequences
Autor/es | Ammar-Khodja, Farid
Benabdallah, Assia González Burgos, Manuel Teresa de Oteyza, María de la Luz de |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2014-10-01 |
Fecha de depósito | 2016-09-28 |
Publicado en |
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Resumen | Let (A, D(A)) a diagonalizable generator of a C0−semigroup of contractions on a complex Hilbert space X, B2L(C, Y ), Y being some suitable extrapolation space of X, and u 2 L2 (0, T; C). Under some assumptions on the ... Let (A, D(A)) a diagonalizable generator of a C0−semigroup of contractions on a complex Hilbert space X, B2L(C, Y ), Y being some suitable extrapolation space of X, and u 2 L2 (0, T; C). Under some assumptions on the sequence of eigenvalues Λ = {λk}k≥1 ⇢ C of (A, D(A)), we prove the existence of a minimal time T0 2 [0, 1] depending on Bernstein’s condensation index of Λ and on B such that y 0 = Ay+Bu is null-controllable at any time T >T0 and not null-controllable for T <T0. As a consequence, we solve controllability problems of various systems of coupled parabolic equations. In particular, new results on the boundary controllability of one-dimensional parabolic systems are derived. These seem to be difficult to achieve using other classical tools. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España Universidad Autónoma de México (UNAM) |
Identificador del proyecto | MTM2010-15592
IN108211 |
Cita | Ammar-Khodja, F., Benabdallah, A., González Burgos, M. y Teresa de Oteyza, M.d.l.L.d. (2014). Minimal time for the null controllability of parabolic systems: the effect of the condensation index of complex sequences. Journal of Functional Analysis, 267 (1), 2077-2151. |
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