Regularity of wave and plate equations with interior point control

Roberto Triggiani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 4, page 307-315
  • ISSN: 1120-6330

Abstract

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The regularity of solutions of various dynamical equations (wave, Euler-Bernoulli, Kirchhoff, Schrödinger) in a bounded open domain Ω in R N , subject to the action of a point control at some point of Ω , is studied. Detailed proofs of the results are contained in the references [8-10].

How to cite

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Triggiani, Roberto. "Regularity of wave and plate equations with interior point control." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.4 (1991): 307-315. <http://eudml.org/doc/244190>.

@article{Triggiani1991,
abstract = {The regularity of solutions of various dynamical equations (wave, Euler-Bernoulli, Kirchhoff, Schrödinger) in a bounded open domain \( \Omega \) in \( \mathbb\{R\}^\{N\} \), subject to the action of a point control at some point of \( \Omega \), is studied. Detailed proofs of the results are contained in the references [8-10].},
author = {Triggiani, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Control Theory; Wave and plate equations; Regularity; regularity of solutions; dynamical equations},
language = {eng},
month = {12},
number = {4},
pages = {307-315},
publisher = {Accademia Nazionale dei Lincei},
title = {Regularity of wave and plate equations with interior point control},
url = {http://eudml.org/doc/244190},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Triggiani, Roberto
TI - Regularity of wave and plate equations with interior point control
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/12//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 4
SP - 307
EP - 315
AB - The regularity of solutions of various dynamical equations (wave, Euler-Bernoulli, Kirchhoff, Schrödinger) in a bounded open domain \( \Omega \) in \( \mathbb{R}^{N} \), subject to the action of a point control at some point of \( \Omega \), is studied. Detailed proofs of the results are contained in the references [8-10].
LA - eng
KW - Control Theory; Wave and plate equations; Regularity; regularity of solutions; dynamical equations
UR - http://eudml.org/doc/244190
ER -

References

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  1. LIONS, J. L., Exact controllability, stabilization and perturbations for distributed systems. SIAM Review, vol. 30, 1988, 1-68. Zbl0644.49028MR931277DOI10.1137/1030001
  2. LIONS, J. L., Pointwise control for distributed systems. SIAM Publication, to appear (based on colloquium given at Workshop held in Tampa, Florida, February 1985). MR2034179
  3. LIONS, J. L., Control des systèmes distribués singuliers. Gauthier Villars, 1983. Zbl0514.93001MR712486
  4. LASIECKA, I. - LIONS, J. L. - TRIGGIANI, R., Nonhomogeneous boundary value problems for second-order hyperbolic operators. J. Math. Pures et Appliques, 65, 1986, 149-192. Zbl0631.35051MR867669
  5. LASIECKA, I. - TRIGGIANI, R., A cosine operator approach to modeling L 2 ⁢ 0 , T ; L 2 ⁢ Γ -boundary input hyperbolic equations. Appl. Math. and Optimiz., 7, 1981, 35-83. Zbl0473.35022MR600559DOI10.1007/BF01442108
  6. LASIECKA, I. - TRIGGIANI, R., Regularity of hyperbolic equations under L 2 ⁢ 0 , T ; L 2 ⁢ Γ -Dirichlet boundary terms. Appl. Math. and Optimiz., 10, 1983, 275-286. Zbl0526.35049MR722491DOI10.1007/BF01448390
  7. MEYER, Y., 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, Boston1985, 234-242. Zbl0543.35030MR879465
  8. TRIGGIANI, R., Regularity with interior point control. Part I: Wave equations and Euler-Bernoulli equations. Lecture notes in mathematics, Spinger-Verlag, to appear. Zbl0800.93596
  9. TRIGGIANI, R., Regularity with interior point control. Part II: Kirchhoff equations. J. Diff. Eq., to appear. Zbl0800.93596
  10. TRIGGIANI, R., Regularity with interior point control. Part III: Schrödinger equations. J. Mathem. Analysis & Applic., to appear. Zbl0800.93596

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