A mathematical aspect of inverse problems for non-stationary Maxwell's equations

International Journal of Applied Electromagnetics and Mechanics

Volumn 8, Issue 1, 1997, Pages 77-98

  Yamamoto, Masahiro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; INVERSE PROBLEMS; STATE ESTIMATION;

ELECTROMAGNETIC PARAMETERS;

MAXWELL EQUATIONS;

EID: 0031101205     PISSN: 13835416     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (63)

1. G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
2. J.A. Stratton, Electromagnetic Theory, McGraw-Hill, New York, 1941.
3. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, Berlin, 1992.
4. P. Neittaanmäki, M. Rudnicki and A. Savini, Inverse Problems and Optimal Design in Electricity and Magnetism, Clarendon Press, Oxford, 1996.
5. A.G. Tijhuis, Electromagnetic Inverse Profiling, VNU Science Press, Utrecht, 1987.
6. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover, New York, 1952.
7. O.A. Ladyzhenskaya and V.A. Solonnikov, J. Sov. Math. 8 (1977), 384.
8. I.G. Petrovkii, Partial Differential Equations, Iliffe Books, London, 1967.
9. M.M. Lavrent'ev, V.G. Romanov and S.P. Shishat-skiǐ, Ill-posed Problems of Mathematical Physics and Analysis, American Mathematical Society, Providence, Rhode Island, 1986.
10. D.L. Russell, SIAM Rev. 20 (1978), 639.
11. Y. Sakawa, SIAM J. Control Opt. 13 (1975), 14.
12. Y. Sakawa, Keisoku Jidô Seigyo-Gakkai Ronbunsyû 12 (1976), 251, in Japanese.
13. T. Suzuki and M. Yamamoto, Jpn. J. Appl. Math. 2 (1985), 211.
14. R. Triggiani, SIAM J. Control Opt. 14 (1976), 313.
15. A. Bensoussan, in: Differential Equations and Control Theory, V. Barbu, ed., Pitman, Boston, 1991, pp. 17-29.
16. K.A. Kime, SIAM J. Control Opt. 28 (1990), 294.
17. V. Komornik, PanAm. Math. J. 4 (1994), 47.
18. J.E. Lagnese, SIAM J. Control Opt. 27 (1989), 374.
19. D.L. Russell, SIAM J. Control Opt. 24 (1986), 199.
20. Q. Zhou, to appear in Jpn. J. Ind. Appl. Math. 19 (1997).
21. R.A. Adams, Soholev Spaces, Academic Press, New York, 1975.
22. O. Nalin, C. R. Acad. Sci. Paris 309 (1989), 811.
23. Q. Zhou and M. Yamamoto, to appear in Int. J. Control.
24. V. Isakov, Inverse Source Problems, American Mathematical Society, Providence, Rhode Island, 1990.
25. J. Rauch, Partial Differential Equations, Springer-Verlag, Berlin, 1991.
26. J.L. Lions, Contrôlabilité Exacte Perturbations et Stabilisation de Systèmes Distribués, Vol. 1, Masson, Paris, 1988.
27. M. Yamamoto, Inverse Probl. 11 (1995), 481.
28. M. Grasselli and M. Yamamoto, to appear.
29. M. Yamamoto, in: Recent Trends of Inverse and Ill-posed Problems, Y. Iso and M. Yamamoto, eds, VSP, Utrecht, 1996, to appear.
30. A.L. Bukhgeim and M.V. Klibanov, Sov. Math. Dokl. 24 (1981), 244.
31. V. Isakov, Inverse Probl. 9 (1993), 579.
32. M.V. Klibanov, Inverse Probl. 8 (1992), 575.
33. M. Kubo, Proc. Jpn Acad. Sci. 71 (1995), 174.
34. J.P. Puel and M. Yamamoto, C. R. Acad. Sci. Paris 320 (1995), 1171.
35. J.P. Puel and M. Yamamoto, in: Control of Partial Differential Equations and Applications, E. Casas, ed., Marcel Dekker, New York, 1995, pp. 241-249.
36. J.P. Puel and M. Yamamoto, J. Inverse Ill-Posed Probl. 5 (1997), 55.
37. M. Yamamoto, to appear in Kôkyû-roku of RIMS, Kyoto University, 1997.
38. H.W. Engl, O. Scherzer and M. Yamamoto, Inverse Probl. 10 (1994), 1253.
39. M.M. Lavrent'ev, K.G. Reznitskaja and V.O. Yakhno, One-dimensional Inverse Problems of Mathematical Physics, American Mathematical Society, Providence, Rhode Island, 1986.
40. V.G. Romanov, Integral Geometry and Inverse Problems for Hyperbolic Equations, Springer-Verlag, Berlin, 1974.
41. V.G. Romanov, Inverse Problems of Mathematical Physics, VNU Science Press, Utrecht, 1987.
42. T. Suzuki, Inverse Probl. 4 (1988), 273.
43. M. Yamamoto, in: Kôkyû-roku of RIMS, Vol. 562, Kyoto University, 1985, pp. 132-166, in Japanese.
44. S. Nakagiri, Inverse Probl. 9 (1993), 143.
45. V.G. Romanov, Sov. Math. Dokl. 19 (1978), 1154.
46. M.M. Lavrent'ev, Some Improperly Posed Problems of Mathematical Physics, Springer-Verlag, Berlin, 1967.
47. A.S. Blagoveshchenskij, Tr. Mat. Inst. Im. V.A. Steklova (Leningrad) 65 (1971), 28.
48. S.I. Kabanikhin and M. Yamamoto, to appear.
49. V. Isakov, in: Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing and W. Rundell, eds, SIAM, Philadelphia, 1990, pp. 203-214.
50. Rakesh and W.W. Symes, Commun. Partial Diff. Eq. 13 (1988), 87.
51. G. Nakamura and G. Uhlmann, SIAM J. Math. Anal. 26 (1995), 263.
52. J. Sylvester and G. Uhlmann, in: Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing and W. Rundell, eds, SIAM, Philadelphia, 1990, pp. 101-139.
53. V. Vogelsang, Math. Ann. 289 (1991), 285.
54. V.G. Romanov and S.I. Kabanikhin, Inverse Problems for Maxwell's Equations, VSP, Utrecht, 1994.
55. V.G. Romanov, in: Ill-posed Problems in Natural Sciences, A.N. Tikhonov, ed., VSP, Utrecht, 1992, pp. 408-416.
56. Z. Sun and G. Uhlmann, Arch. Rat. Mech. Anal. 119 (1992), 71.
57. P. Ola, L. Päivärinta and E. Somersalo, Duke Math. J. 70 (1993), 617.
58. A. Lorenzi and V.G. Romanov, Inverse Probl. 9 (1993), 301.
59. V. Romanov, J. Inverse Ill-Posed Probl. 3 (1995), 321.
60. S.I. Kabanikhin and A. Lorenzi, Inverse Probl. 7 (1991), 863.
61. R. Courant and D. Hubert, Methods of Mathematical Physics, Interscience, New York, 1953, 1961.
62. K. Yosida, Functional Analysis, Springer-Verlag, Berlin, 1971.
63. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.