Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons

Mikhail Belishev; Aleksandr Glasman

ESAIM: Control, Optimisation and Calculus of Variations (2000)

  • Volume: 5, page 207-217
  • ISSN: 1292-8119

How to cite

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Belishev, Mikhail, and Glasman, Aleksandr. "Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 207-217. <http://eudml.org/doc/90568>.

@article{Belishev2000,
author = {Belishev, Mikhail, Glasman, Aleksandr},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {unreachable states; topology of a domain},
language = {eng},
pages = {207-217},
publisher = {EDP Sciences},
title = {Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons},
url = {http://eudml.org/doc/90568},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Belishev, Mikhail
AU - Glasman, Aleksandr
TI - Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 207
EP - 217
LA - eng
KW - unreachable states; topology of a domain
UR - http://eudml.org/doc/90568
ER -

References

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  2. [2] M.I. Belishev, Boundary control in reconstruction of manifolds and metrics(the BC-method). Inverse Problems 13 ( 1997) R1-R45. http://www.iop.org/Journals/ip/. Zbl0990.35135MR1474359
  3. [3] M. Belishev and A. Glasman, Boundary control and inverse problem for the dynamical maxwell system: the recovering of velocity in regular zone. Preprint CMLA ENS Cachan ( 1998) 9814. http://www.cmla.ens-cachan.fr Zbl1012.78010
  4. [4] M. Belishev and A. Glasman, Vizualization of waves in the Maxwell dynamical system(The BC-method). Preprint POMI ( 1997) 22. http://www.pdmi.ras.ru/preprint/1997/ MR1701858
  5. [5] M. Belishev, V. Isakov, L. Pestov and V. Sharafutdinov, On reconstruction of gravity field via external electromagnetic measurements. Preprint PDMI ( 1999) 10.http://www.pdmi.ras.ru/preprint/1999/10-99.ps.gz. Zbl1048.35132
  6. [6] E.B. Bykhovskii and N.V. Smirnov, On an orthogonal decomposition of the space of square-summable vector- functions and operators of the vector analisys. Proc. Steklov Inst. Math. 59 ( 1960) 5-36, in Russian. Zbl0104.15504MR121641
  7. [7] G. Duvaut and J.L. Lions, Les inéquations en mécanique et en physique, Vol. 21 of Travaux et recherches mathématiques. Paris: Dunod. XX ( 1972). Zbl0298.73001MR464857
  8. [8] M. Eller, V. Isakov, G. Nakamura and D. Tataru, Uniqueness and stability in the Cauchy Problem for Maxwell and elasticity systems. Nonlinear Partial Differential Equations and their applications. College de France Seminar. XIV ( 1999) to appear. Zbl1038.35159MR1936000
  9. [9] J. Lagnese, Exact boundary controllability of Maxwell's equations in a general region. SIAM J. Control Optim. 27 ( 1989) 374-388. Zbl0678.49032MR984833
  10. [10] I. Lasiecka and R. Triggiani, Recent advances in regularity of second-order hyperbolic mixed problems, and applications, K.R.T. Christopher et al., Eds. Jones, editor. Springer-Verlag, Berlin, Dynam. Report. Expositions Dynam. Systems (N.S.) 3 ( 1994) 104-162. Zbl0807.35080MR722491
  11. [11] R. Leis, Initial boundary value problems in mathematical physics. Teubner, Stuttgart ( 1972). Zbl0599.35001MR841971
  12. [12] V.G. Maz'ya, The Sobolev spaces. Leningrad, Leningrad State University ( 1985), in Russian. Zbl0727.46017MR807364
  13. [13] O. Nalin, Controlabilité exacte sur une partie du bord des équations de Maxwell. C. R. Acad. Sci. Paris Sér. I Math. 309 ( 1989) 811-815. Zbl0688.49041MR1055200
  14. [14] D.L. Russell, Boundary value control theory of the higher-dimensional wave equation. SIAM J. Control Optim. 9 ( 1971) 29-42. Zbl0204.46201MR274917
  15. [15] G. Schwarz, Hodge decomposition. A method for solving boundary value problems. Springer Verlag, Berlin, Lecture Notes in Math. 1607 ( 1995). Zbl0828.58002MR1367287
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  17. [17] N. Week, Exact boundary controllability of a Maxwell problem. SIAM J. Control Optim. (to appear). Zbl0963.93040

Citations in EuDML Documents

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  1. M. I. Belishev, I. Lasiecka, The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation
  2. M. I. Belishev, I. Lasiecka, The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation
  3. John E. Lagnese, G. Leugering, Time Domain Decomposition in Final Value Optimal Control of the Maxwell System
  4. John E. Lagnese, G. Leugering, Time domain decomposition in final value optimal control of the Maxwell system

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