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

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1. [1] S. Avdonin, M. Belishev and S. Ivanov, The controllability in the filled domain for the multidimensional wave equation with a singular boundary control J. Math. Sci. 83 ( 1997). Zbl0870.93004MR1334739
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
16. [16] D. Tataru, Unique continuation for solutions to PDE's; between Hoermander's theorem and Holmgren's theorem. Comm. Partial Differential Equations 20 ( 1995) 855-884. Zbl0846.35021MR1326909
17. [17] N. Week, Exact boundary controllability of a Maxwell problem. SIAM J. Control Optim. (to appear). Zbl0963.93040

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