Triggiani: Regularity of wave and plate equations with interior point control

Triggiani, Roberto:
Regularity of wave and plate equations with interior point control (Regolarità delle equazioni delle onde e delle piastre con controllo puntuale interno)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 2 (1991), fasc. n.4, p. 307-315, (English)
pdf (785 Kb), djvu (186 Kb). | MR1152637 | Zbl 0756.93034

Sunto

Si studia la regolarità delle soluzioni di varie equazioni dinamiche (onde, Euler-Bernoulli, Kirchhoff, Schrödinger) in una regione limitata \( \Omega \) di \( \mathbb{R}^{N} \), sotto l'azione di un controllo esercitato in un punto di \( \Omega \). Le dimostrazioni dettagliate si trovano nei riferimenti bibliografici [8-10].

Referenze Bibliografiche

[1] J. L. LIONS, Exact controllability, stabilization and perturbations for distributed systems. SIAM Review, vol. 30, 1988, 1-68. | fulltext (doi) | MR 931277 | Zbl 0644.49028

[2] J. L. LIONS, Pointwise control for distributed systems. SIAM Publication, to appear (based on colloquium given at Workshop held in Tampa, Florida, February 1985). | MR 2034179

[3] J. L. LIONS, Control des systèmes distribués singuliers. Gauthier Villars, 1983. | MR 712486 | Zbl 0514.93001

[4] I. LASIECKA - J. L. LIONS - R. TRIGGIANI, Nonhomogeneous boundary value problems for second-order hyperbolic operators. J. Math. Pures et Appliques, 65, 1986, 149-192. | MR 867669 | Zbl 0631.35051

[5] I. LASIECKA - R. TRIGGIANI, A cosine operator approach to modeling \( L_{2} (0,T;L_{2}(\Gamma)) \)-boundary input hyperbolic equations. Appl. Math. and Optimiz., 7, 1981, 35-83. | fulltext (doi) | MR 600559 | Zbl 0473.35022

[6] I. LASIECKA - R. TRIGGIANI, Regularity of hyperbolic equations under \( L_{2} (0,T;L_{2}(\Gamma)) \)-Dirichlet boundary terms. Appl. Math. and Optimiz., 10, 1983, 275-286. | fulltext (doi) | MR 722491 | Zbl 0526.35049

[7] Y. MEYER, Etude d'un modèle mathématique issu du contrôle des structures spatiales déformables. In: H. BREZIS - J. L. LIONS (eds.), Nonlinear Partial Differential Equations and their Applications. College de France Seminar, vol. II, Research Notes in Mathematics, Pitman, Boston 1985, 234-242. | MR 879465 | Zbl 0543.35030

[8] R. TRIGGIANI, Regularity with interior point control. Part I: Wave equations and Euler-Bernoulli equations. Lecture notes in mathematics, Spinger-Verlag, to appear. | Zbl 0800.93596

[9] R. TRIGGIANI, Regularity with interior point control. Part II: Kirchhoff equations. J. Diff. Eq., to appear. | Zbl 0800.93596

[10] R. TRIGGIANI, Regularity with interior point control. Part III: Schrödinger equations. J. Mathem. Analysis & Applic., to appear. | Zbl 0800.93596

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche