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oai:docta.ucm.es:20.500.14352/569982023-08-25T17:38:57Zcom_20.500.14352_14col_20.500.14352_15

Controllability of star-shaped networks of strings Zuazua Iriondo, Enrique Dáger Salomón, René 519.6 Control acts on the junction point Observability inequality Análisis numérico 1206 Análisis Numérico In this note we consider a star-shaped network of vibrating strings. The problem of controllability when one control acts on the junction point is considered. A simple proof is given that, in particular, does not use Ingham inequalities, of the fact that the set of reachable data is dense, whenever the lengths of the strings are mutually irrational. The proof is based on an observability inequality with suitable weights on the Fourier coefficients that is easily obtained as a consequence of the time-periodicity of the solutions. Those weights can be estimated under certain algebraicity conditions imposed on the lengths of the strings. This allows to proof exact controllability results in Sobolev spaces of appropriate order. Further results are also presented concerning the control from a free end and diffusion processes. DGES EU TMR Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:47:16Z 2023-06-20T16:47:16Z 2001-04-01 journal article https://hdl.handle.net/20.500.14352/56998 0764-4442 10.1016/S0764-4442(01)01876-6 eng PB96-0663 Homogenization and Multiple Scales open access application/pdf Elsevier