On the Controllability for Second Order Hyperbolic Equations in Curved Polygons

Authors

  • W.D. Bastos
  • A. Spezamiglio

DOI:

https://doi.org/10.5540/tema.2007.08.02.0169

Abstract

In this work we study exact boundary controllability for a class of hyperbolic linear partial differential equation with constant coefficient which includes the linear Klein-Gordon equation. We consider piecewise smooth domains on the plane, initial state with finite energy and control of Robin type, acting on the whole boundary or only on a part of it.

References

[1] C. Bardos, G. Lebeau, J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim., 30 (1992), 1024-1065.

W.D. Bastos, A. Spezamiglio, A note on the controllability for the wave equation on nonsmooth plane domains. Systems Control Lett. 55 (2006), 17-20.

P. Grisvard, Controlabilit´e exacte des solutions de l ’equation des ondes en pr´esence de singularit´es. J. Math. Pures Appl., 68 (1989), 215-259.

J.-L. Lions, Contrˆolabilit´e exacte des syst`emes distribu´es. C. R. Math. Acad. Sci. Paris, Ser. I Math., 302 (1986), 471-475.

W. Littman, Near Optimal Time Boundary Controllability for a Class of Hyperbolic Equations, In “Lecture Notes in Control and Inform. Sci.”, p.306-312, Springer, New York, 1987.

W. Littman, Remarks on Boundary Control for Polyhedral Domains and Related Results, in “Boundary Control and Boundary Variation”, (J.P. Zol´ezio, ed.), p.272-284, Springer, New York, 1990.

D.L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Stud. Appl. Math., 52 (1973), 189-211.

D. Tataru, On the regularity of boundary traces for the wave equation. Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 26 (1998), 185-206.

J. Wrokla, “Partial Differential Equations”, Cambridge University Press, 1987.

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Published

2007-08-13

How to Cite

Bastos, W., & Spezamiglio, A. (2007). On the Controllability for Second Order Hyperbolic Equations in Curved Polygons. Trends in Computational and Applied Mathematics, 8(2), 169–179. https://doi.org/10.5540/tema.2007.08.02.0169

Issue

Vol. 8 No. 2 (2007)

Section

Original Article

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