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A remark on Littman's method of boundary controllability
1. | Department of Mathematics, Georgetown University, Washington, DC 20057 |
References:
[1] |
M. Atiyah, R. Bott and L. G$\dota$rding, Lacunas for hyperbolic differential operators with constant coefficients. I,, Acta Mathematica, 124 (1970), 109.
doi: 10.1007/BF02394570. |
[2] |
M. Atiyah, R. Bott and L. G$\dota$rding, Lacunas for hyperbolic differential operators with constant coefficients. II,, Acta Mathematica, 131 (1973), 145.
doi: 10.1007/BF02392039. |
[3] |
L. Ahlfors, Complex Analysis,, An introduction to the theory of analytic functions of one complex variable. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., (1978).
|
[4] |
F. Alabau and V. Komornik, Boundary observability, controllability, and stabilization of linear elastodynamic systems,, SIAM Journal on Control and Optimization, 37 (1999), 521.
doi: 10.1137/S0363012996313835. |
[5] |
C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary,, SIAM Journal on Control and Optimization, 30 (1992), 1024.
doi: 10.1137/0330055. |
[6] |
M. Eller, V. Isakov, G. Nakamura and D. Tataru, Uniqueness and stability in the Cauchy problem for Maxwell and elasticity systems,, in Studies in Mathematics and its Applications, 31 (2002), 329.
doi: 10.1016/S0168-2024(02)80016-9. |
[7] |
M. Eller, Continuous observability for the anisotropic Maxwell system,, Applied Mathematics and Optimization, 55 (2007), 185.
doi: 10.1007/s00245-006-0886-x. |
[8] |
M. Eller and D. Toundykov, A global Holmgren theorem for multidimensional hyperbolic partial differential equations,, Applicable Analysis, 91 (2012), 69.
doi: 10.1080/00036811.2010.538685. |
[9] |
R. Gulliver and W. Littman, Chord uniqueness and controllability: The view from the boundary. I,, in Contemporary Mathematics, 268 (2000), 145.
doi: 10.1090/conm/268/04312. |
[10] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations Of Second Order,, second edition, (1983).
|
[11] |
L. Ho, Observabilité frontière de l'équation des ondes,, Comptes Rendus des Séances de l'Académie des Sciences. Série I. Mathématique, 302 (1986), 443.
|
[12] |
L. Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations,, L'Enseignement Mathématique. Revue Internationale. IIe Série, 17 (1971), 99.
|
[13] |
L. Hörmander, The Analysis Of Linear Partial Differential Operators. I,, Distribution theory and Fourier analysis. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], (1983).
|
[14] |
L. Hörmander, The Analysis Of Linear Partial Differential Operators. II,, Differential operators with constant coefficients. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], (1983).
doi: 10.1007/978-3-642-96750-4. |
[15] |
M. A. Horn, Exact controllability of the Euler-Bernoulli plate via bending moments only on the space of optimal regularity,, Journal of Mathematical Analysis and Applications, 167 (1992), 557.
doi: 10.1016/0022-247X(92)90224-2. |
[16] |
F. John, Partial Differential Equations,, fourth edition, (1991).
|
[17] |
J. E. Lagnese, Exact boundary controllability of Maxwell's equations in a general region,, SIAM Journal on Control and Optimization, 27 (1989), 374.
doi: 10.1137/0327019. |
[18] |
I. Lasiecka and R. Triggiani, Exact controllability of the wave equation with Neumann boundary control,, Applied Mathematics and Optimization, 19 (1989), 243.
doi: 10.1007/BF01448201. |
[19] |
I. Lasiecka and R. Triggiani, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions,, Applied Mathematics and Optimization, 25 (1992), 189.
doi: 10.1007/BF01182480. |
[20] |
I. Lasiecka, R. Triggiani and X. Zhang, Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot,, in Contemporary Mathematics, 268 (2000), 227.
doi: 10.1090/conm/268/04315. |
[21] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems,, SIAM Review, 30 (1988), 1.
doi: 10.1137/1030001. |
[22] |
W. Littman, Near optimal time boundary controllability for a class of hyperbolic equations,, in Lecture Notes in Control and Information Science, 97 (1987), 307.
doi: 10.1007/BFb0038763. |
[23] |
W. Littman, A remark on boundary control on manifolds,, in Lecture Notes in Pure and Applied Mathematics, 242 (2005), 175.
doi: 10.1201/9781420028317.ch11. |
[24] |
W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory,, Journal d'Analyse Mathématique, 59 (1992), 117.
doi: 10.1007/BF02790221. |
[25] |
R. Melrose and G. Uhlmann, Microlocal structure of involutive conical refraction,, Duke Mathematical Journal, 46 (1979), 571.
doi: 10.1215/S0012-7094-79-04630-1. |
[26] |
N. Ortner and P. Wagner, On conical refraction in hexagonal and cubic media,, SIAM Journal on Applied Mathematics, 70 (2009), 1239.
doi: 10.1137/080736636. |
[27] |
D. Russell, Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions,, SIAM Review, 20 (1978), 639.
doi: 10.1137/1020095. |
[28] |
R. Sakamoto, Hyperbolic Boundary Value Problems,, Translated from the Japanese by Katsumi Miyahara. Cambridge University Press, (1982).
|
[29] |
D. Tataru, Boundary controllability for conservative PDEs,, Applied Mathematics and Optimization, 31 (1995), 257.
|
[30] |
D. Tataru, On the regularity of boundary traces for the wave equation,, Annali della Scuola Normale Superiore di Pisa, 26 (1998), 185.
|
[31] |
M. Taylor, Pseudodifferential Operators,, Princeton Mathematical Series, (1981).
|
[32] |
R. Triggiani, Regularity theory, exact controllability, and optimal quadratic cost problem for spherical shells with physical boundary controls,, Control and Cybernetics, 25 (1996), 553.
|
show all references
References:
[1] |
M. Atiyah, R. Bott and L. G$\dota$rding, Lacunas for hyperbolic differential operators with constant coefficients. I,, Acta Mathematica, 124 (1970), 109.
doi: 10.1007/BF02394570. |
[2] |
M. Atiyah, R. Bott and L. G$\dota$rding, Lacunas for hyperbolic differential operators with constant coefficients. II,, Acta Mathematica, 131 (1973), 145.
doi: 10.1007/BF02392039. |
[3] |
L. Ahlfors, Complex Analysis,, An introduction to the theory of analytic functions of one complex variable. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., (1978).
|
[4] |
F. Alabau and V. Komornik, Boundary observability, controllability, and stabilization of linear elastodynamic systems,, SIAM Journal on Control and Optimization, 37 (1999), 521.
doi: 10.1137/S0363012996313835. |
[5] |
C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary,, SIAM Journal on Control and Optimization, 30 (1992), 1024.
doi: 10.1137/0330055. |
[6] |
M. Eller, V. Isakov, G. Nakamura and D. Tataru, Uniqueness and stability in the Cauchy problem for Maxwell and elasticity systems,, in Studies in Mathematics and its Applications, 31 (2002), 329.
doi: 10.1016/S0168-2024(02)80016-9. |
[7] |
M. Eller, Continuous observability for the anisotropic Maxwell system,, Applied Mathematics and Optimization, 55 (2007), 185.
doi: 10.1007/s00245-006-0886-x. |
[8] |
M. Eller and D. Toundykov, A global Holmgren theorem for multidimensional hyperbolic partial differential equations,, Applicable Analysis, 91 (2012), 69.
doi: 10.1080/00036811.2010.538685. |
[9] |
R. Gulliver and W. Littman, Chord uniqueness and controllability: The view from the boundary. I,, in Contemporary Mathematics, 268 (2000), 145.
doi: 10.1090/conm/268/04312. |
[10] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations Of Second Order,, second edition, (1983).
|
[11] |
L. Ho, Observabilité frontière de l'équation des ondes,, Comptes Rendus des Séances de l'Académie des Sciences. Série I. Mathématique, 302 (1986), 443.
|
[12] |
L. Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations,, L'Enseignement Mathématique. Revue Internationale. IIe Série, 17 (1971), 99.
|
[13] |
L. Hörmander, The Analysis Of Linear Partial Differential Operators. I,, Distribution theory and Fourier analysis. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], (1983).
|
[14] |
L. Hörmander, The Analysis Of Linear Partial Differential Operators. II,, Differential operators with constant coefficients. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], (1983).
doi: 10.1007/978-3-642-96750-4. |
[15] |
M. A. Horn, Exact controllability of the Euler-Bernoulli plate via bending moments only on the space of optimal regularity,, Journal of Mathematical Analysis and Applications, 167 (1992), 557.
doi: 10.1016/0022-247X(92)90224-2. |
[16] |
F. John, Partial Differential Equations,, fourth edition, (1991).
|
[17] |
J. E. Lagnese, Exact boundary controllability of Maxwell's equations in a general region,, SIAM Journal on Control and Optimization, 27 (1989), 374.
doi: 10.1137/0327019. |
[18] |
I. Lasiecka and R. Triggiani, Exact controllability of the wave equation with Neumann boundary control,, Applied Mathematics and Optimization, 19 (1989), 243.
doi: 10.1007/BF01448201. |
[19] |
I. Lasiecka and R. Triggiani, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions,, Applied Mathematics and Optimization, 25 (1992), 189.
doi: 10.1007/BF01182480. |
[20] |
I. Lasiecka, R. Triggiani and X. Zhang, Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot,, in Contemporary Mathematics, 268 (2000), 227.
doi: 10.1090/conm/268/04315. |
[21] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems,, SIAM Review, 30 (1988), 1.
doi: 10.1137/1030001. |
[22] |
W. Littman, Near optimal time boundary controllability for a class of hyperbolic equations,, in Lecture Notes in Control and Information Science, 97 (1987), 307.
doi: 10.1007/BFb0038763. |
[23] |
W. Littman, A remark on boundary control on manifolds,, in Lecture Notes in Pure and Applied Mathematics, 242 (2005), 175.
doi: 10.1201/9781420028317.ch11. |
[24] |
W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory,, Journal d'Analyse Mathématique, 59 (1992), 117.
doi: 10.1007/BF02790221. |
[25] |
R. Melrose and G. Uhlmann, Microlocal structure of involutive conical refraction,, Duke Mathematical Journal, 46 (1979), 571.
doi: 10.1215/S0012-7094-79-04630-1. |
[26] |
N. Ortner and P. Wagner, On conical refraction in hexagonal and cubic media,, SIAM Journal on Applied Mathematics, 70 (2009), 1239.
doi: 10.1137/080736636. |
[27] |
D. Russell, Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions,, SIAM Review, 20 (1978), 639.
doi: 10.1137/1020095. |
[28] |
R. Sakamoto, Hyperbolic Boundary Value Problems,, Translated from the Japanese by Katsumi Miyahara. Cambridge University Press, (1982).
|
[29] |
D. Tataru, Boundary controllability for conservative PDEs,, Applied Mathematics and Optimization, 31 (1995), 257.
|
[30] |
D. Tataru, On the regularity of boundary traces for the wave equation,, Annali della Scuola Normale Superiore di Pisa, 26 (1998), 185.
|
[31] |
M. Taylor, Pseudodifferential Operators,, Princeton Mathematical Series, (1981).
|
[32] |
R. Triggiani, Regularity theory, exact controllability, and optimal quadratic cost problem for spherical shells with physical boundary controls,, Control and Cybernetics, 25 (1996), 553.
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