Inverse problems for heat equations on compact intervals and on circles, I

Takashi SUZUKI

doi:10.2969/jmsj/03810039

Takashi SUZUKI

著者情報

ジャーナルフリー

1986 年 38 巻 1 号 p. 39-65

DOI https://doi.org/10.2969/jmsj/03810039

詳細

Published: 1986 Received: 1982/05/18 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math., 78 (1946), 1-96.
2) I. M. Gel'fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Amer. Math. Soc. Transl., (2) 1 (1955), 253-304.
3) H. Hochstadt, The inverse Sturm-Liouville problem, Comm. Pure Appl. Math., 26 (1973), 715-729.
4) H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math., 34 (1978), 676-680.
5) S. Kitamura and S. Nakagiri, Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type, SIAM J. Control Optimization, 15 (1977), 785-802.
6) N. Levinson, The inverse Sturm-Liouville problem, Mat. Tidsskr. B., (1949), 25-30.
7) B. M. Levitan and M. G. Gasymov, Determination of a differential equation by two of its spectra, Russian Math. Survey, 19-2 (1964), 1-63.
8) B. M. Levitan and I. S. Sargsjan, Introduction to spectral theory, Transl. Math. Monographs, 39, Amer. Math. Soc., 1975.
9) R. Murayama, The Gel'fand-Levitan theory and certain inverse problems for the parabolic equation, J. Fac. Sci. Univ. Tokyo, 28 (1981), 317-330.
10) E. Picard, Leçons sur quelques types simples d'equations aux dérivées partielles,Gauthier-Villars, 1950.
11) A. Pierce, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. Control Optimization, 17 (1979), 494-499.
12) T. I. Seidman, Ill-posed problems arising in boundary control and observation for diffusion equations, in Inverse and Improperly Posed Problems in Differential Equations, edited by G. Anger, Akademie-Verlag, 1979, 233-247.
13) T. Suzuki, Uniqueness and nonuniqueness in an inverse problem for the parabolic equation, J. Differential equations, 47 (1983), 296-316.
14) T. Suzuki, Inverse problems for the heat equation (in Japanese), Sugaku, 34 (1982), 55-64.
15) T. Suzuki, Uniqueness and nonuniqueness in an inverse problem for parabolic equations, in Computing Methods in Applied Sciences and Engineering, V, edited by R. Glowinski and J. L. Lions, North-Holland, 1982, 659-668.
16) T. Suzuki, Remarks on the uniqueness in an inverse problem for the heat equation, I and II, Proc. Japan Acad. Ser. A., 58 (1982), 93-96 and 175-177.
17) T. Suzuki and R. Murayama, A uniqueness theorem in an identification problem for coefficients of parabolic equations, Proc. Japan Acad., 56 (1980), 259-263.
18) T. Suzuki, Gel'fand-Levitan's theory, deformation formulas and inverse problems, to appear in J. Fac. Sci. Univ. Tokyo.

Right : [1] G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math., 78 (1946), 1-96.
[2] I. M. Gel'fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Amer. Math. Soc. Transl., (2) 1 (1955), 253-304.
[3] H. Hochstadt, The inverse Sturm-Liouville problem, Comm. Pure Appl. Math., 26 (1973), 715-729.
[4] H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math., 34 (1978), 676-680.
[5] S. Kitamura and S. Nakagiri, Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type, SIAM J. Control Optimization, 15 (1977), 785-802.
[6] N. Levinson, The inverse Sturm-Liouville problem, Mat. Tidsskr. B., (1949), 25-30.
[7] B. M. Levitan and M. G. Gasymov, Determination of a differential equation by two of its spectra, Russian Math. Survey, 19-2 (1964), 1-63.
[8] B. M. Levitan and I. S. Sargsjan, Introduction to spectral theory, Transl. Math. Monographs, 39, Amer. Math. Soc., 1975.
[9] R. Murayama, The Gel'fand-Levitan theory and certain inverse problems for the parabolic equation, J. Fac. Sci. Univ. Tokyo, 28 (1981), 317-330.
[10] E. Picard, Leçons sur quelques types simples d'equations aux dérivées partielles,Gauthier-Villars, 1950.
[11] A. Pierce, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. Control Optimization, 17 (1979), 494-499.
[12] T. I. Seidman, Ill-posed problems arising in boundary control and observation for diffusion equations, in Inverse and Improperly Posed Problems in Differential Equations, edited by G. Anger, Akademie-Verlag, 1979, 233-247.
[13] T. Suzuki, Uniqueness and nonuniqueness in an inverse problem for the parabolic equation, J. Differential equations, 47 (1983), 296-316.
[14] T. Suzuki, Inverse problems for the heat equation (in Japanese), Sûgaku, 34 (1982), 55-64.
[15] T. Suzuki, Uniqueness and nonuniqueness in an inverse problem for parabolic equations, in Computing Methods in Applied Sciences and Engineering, V, edited by R. Glowinski and J. L. Lions, North-Holland, 1982, 659-668.
[16] T. Suzuki, Remarks on the uniqueness in an inverse problem for the heat equation, I and II, Proc. Japan Acad. Ser. A., 58 (1982), 93-96 and 175-177.
[17] T. Suzuki and R. Murayama, A uniqueness theorem in an identification problem for coefficients of parabolic equations, Proc. Japan Acad., 56 (1980), 259-263.
[18] T. Suzuki, Gel'fand-Levitan's theory, deformation formulas and inverse problems, to appear in J. Fac. Sci. Univ. Tokyo.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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